Finite Mathematics and Applied Calculus 7e Stefan Waner Steven Costenoble - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Determine the dimension of the matrix. a. b. c. d. e. ANSWER: a POINTS: 1 QUESTION TYPE: Multiple …
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Finite Mathematics and Applied Calculus 7e Stefan Waner Steven Costenoble – Test Bank
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Sample Questions Are Posted Below
| 1. Determine the dimension of the matrix.
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| 2. Solve for x and y.
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| 3. If and , then find .
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| 4. If , then find .
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| 5. Perform the indicated operations.
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| 6. The following table shows sales of recreational boats in the United States during the period 1999-2001.
Write the matrix algebra formula that will find the sales in each category.
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| 7. The following tables give annual production costs and profits at Gauss Jordan Sneakers.
Write the matrix algebraic formula to compute the revenues from each sector each year.
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| 8. Let and .
Evaluate A + B.
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| 9. Let , and .
Evaluate .
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| 10. Find the dimensions of the matrix
and identify the value of the element .
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| 11. Find the dimensions of the matrix
and identify the value of the element .
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| 12. Find the dimensions of the matrix
and identify the value of the element .
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| 13. Solve for x, y, and z.
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| 14. Let and . Evaluate .
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| 15. Let and , evaluate .
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| 16. Let and . Evaluate .
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| 17. Let , , and . Evaluate .
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18. The Left Coast Bookstore chain has two stores, one in San Francisco and one in Los Angeles. It stocks three kinds of books: hardcover, softcover, and plastic (for infants). The table shows the number of books in stock at the beginning of January.
Suppose its sales in January were as follows: 700 hardcover books, 1,300 softcover books, and 2,000 plastic books sold in San Francisco, and 400 hardcover, 300 softcover, and 500 plastic books sold in Los Angeles. Now suppose that the stores maintained the same sales figures for the first 6 months of the year. Each month the chain restocked the stores from its warehouse by shipping 900 hardcover, 1,600 softcover, and 1,800 plastic books to San Francisco and 700 hardcover, 700 softcover, and 200 plastic books to Los Angeles. Use matrix operations to determine the inventory in each store at the end of June.
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| 19. Microbucks Computers makes two computers, the Pomegranate II and the Pomegranate Classic, at two different factories. The Pom II requires 2 processor chips, 18 memory chips, and 20 vacuum tubes, and the Pom Classic requires 2 processor chips, 6 memory chips, and 50 vacuum tubes. At the beginning of the year, Microbucks has in stock 800 processor chips, 6,000 memory chips, and 13,000 vacuum tubes at the Pom II factory and 400 processor chips, 4,000 memory chips, and 40,000 vacuum tubes at the Pom Classic factory. It manufactures 50 Pom IIs and 50 Pom Classics each month.
Find the company’s inventory of parts after 2 months, using matrix operations.
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20. The table gives the number of people (in thousands) who visited Australia and South Africa in 1998:
Figures are rounded to the nearest 1,000. You predict that, in 2008, 20,000 fewer people from North America will visit Australia and 30,000 more will visit South Africa, 80,000 more people from Europe will visit each of Australia and South Africa, and 150,000 more people from Asia will visit South Africa, but there will be no change in the number visiting Australia. Use matrix algebra to predict the number of visitors from the three regions to Australia and South Africa in 2008.
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| 21. Solve for x, y, and z.
__________ __________ __________
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| 22. Given the following matrix.
What are the dimensions? ____________________ What is the value of the element ? __________
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| 23. Given the following matrix.
What are the dimensions? What is the value of the element ?
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| 24. Given the following matrix.
What are the dimensions? What is the value of the element ?
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| 25. Solve for x, y, and z.
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| 26. Microbucks Computers makes two computers, the Pomegranate II and the Pomegranate Classic, at two different factories. The Pom II requires 2 processor chips, 18 memory chips, and 40 vacuum tubes, and the Pom Classic requires 1 processor chip, 2 memory chips, and 30 vacuum tubes. At the beginning of the year, Microbucks has in stock 600 processor chips, 9,000 memory chips, and 14,000 vacuum tubes at the Pom II factory and 500 processor chips, 2,000 memory chips, and 40,000 vacuum tubes at the Pom Classic factory. It manufactures 50 Pom IIs and 50 Pom Classics each month.
Find the company’s inventory of parts after 2 months, using matrix operations. Please enter your answer as a matrix in the following form (Do not use commas.):
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| 27. Let and
Evaluate A + B.
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| 28. Let , and
Evaluate .
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| 29. What is the dimension of the matrix?
The dimension of the matrix is . What is the value of the element ?
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30. If , and then find .
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| 1. Find the matrix product, if possible.
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| 2. Find the matrix product, if possible.
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| 3. Given , , and , which of the following can be calculated?
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| 4. Find when .
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| 5. The following matrix equation is equivalent to which system of linear equations?
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6. Editors’ workloads were increasing during the 1990s, as the following table shows.
Which matrix expression would estimate the total number of books edited during the years 1993-1996?
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| 7. Translate the matrix equations into a system of linear equations.
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| 8. Translate the given system of equations into matrix form.
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| 9. Compute the product of the two matrices (if possible).
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| 10. Compute the product of the two matrices (if possible).
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| 11. Compute the product, if possible.
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| 12. Translate the given system of equations into matrix form.
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| 13. Your T-shirt operation is doing a booming trade. Last week you sold 60 tie-dyed shirts for $17 each, 75 Suburban State University crew shirts for $8 each, and 30 lacrosse T-shirts for $11 each. Use matrix operations to calculate your total revenue for the week.
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| 14. Karen Sandberg, your competition in Suburban State U’s T-shirt market, has apparently been undercutting your prices and outperforming you in sales. Last week she sold 120 tie-dyed shirts for $12 each, 80 (low quality) crew shirts at $1 apiece, and 50 lacrosse T-shirts for $6 each. Use matrix operations to calculate her total revenue for the week.
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15. In January, the Left Coast Bookstore chain sold 600 hardcover books, 1,100 softcover books, and 1,800 plastic books in San Francisco; it sold 300 hardcover, 100 softcover, and 300 plastic books in Los Angeles. Hardcover books sell for $32 each, softcover books sell for $7 each, and plastic books sell for $11 each.
Use matrix multiplication to compute the total revenue at the two stores.
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16. In January, the Left Coast Bookstore chain sold 600 hardcover books, 1,100 softcover books, and 1,700 plastic books in San Francisco; it sold 300 hardcover, 100 softcover, and 200 plastic books in Los Angeles. Hardcover books sell for $26 each, softcover books sell for $8 each, and plastic books sell for $15 each.
Suppose that each hardcover book costs the stores $10, each softcover book costs $5, and each plastic book costs $10. Use matrix operations to compute the the total profit at each store in January.
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17. The table shows the cost of one square foot of residential real estate, in dollars per square foot, together with the number of square feet your development company intends to purchase in each city.
Use matrix multiplication to estimate the total cost of the real estate.
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18. The total amount of cheese, in billions of pounds, produced in the western and north central states in 1999 and 2000 was as follows.
Thinking of this table as a (labeled) matrix P, compute the matrix product .
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19. The chart shows the number of personal bankruptcy filings in three City regions during various months of 2001 – 2002.
Write a matrix product whose computation gives the total number by which bankruptcy filings in January, 2001, exceeded filings in January, 2002.
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| 20. Your T-shirt operation is doing a booming trade. Last week you sold 70 tie-dyed shirts for $18 each, 55 Suburban State University crew shirts for $9 each, and 50 lacrosse T-shirts for $14 each.
Use matrix operations to calculate your total revenue for the week. __________
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| 21. Karen Sandberg, your competition in Suburban State U’s T-shirt market, has apparently been undercutting your prices and outperforming you in sales. Last week she sold 160 tie-dyed shirts for $10 each, 95 (low quality) crew shirts at $5 apiece, and 50 lacrosse T-shirts for $7 each.
Use matrix operations to calculate her total revenue for the week. __________
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22. The table shows the cost of one square foot of residential real estate, in dollars per square foot, together with the number of square feet your development company intends to purchase in each city.
Use matrix multiplication to estimate the total cost of the real estate. __________
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| 23. Compute the product of the two matrices (if possible).
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24. In January, the Left Coast Bookstore chain sold 900 hardcover books, 1,200 softcover books, and 1,700 plastic books in San Francisco; it sold 600 hardcover, 500 softcover, and 700 plastic books in Los Angeles. Hardcover books sell for $33 each, softcover books sell for $9 each, and plastic books sell for $13 each.
Use matrix multiplication to compute the the total revenue at the two stores. Please enter your answer as a column matrix in the following form:
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25. In January, the Left Coast Bookstore chain sold 900 hardcover books, 1,200 softcover books, and 1,600 plastic books in San Francisco; it sold 600 hardcover, 500 softcover, and 700 plastic books in Los Angeles. Hardcover books sell for $34 each, softcover books sell for $8 each, and plastic books sell for $14 each.
Suppose that each hardcover book costs the stores $10, each softcover book costs $5, and each plastic book costs $10. Use matrix operations to compute the the total profit at each store in January. Please enter your answer as a column matrix in the following form:
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| 26. Compute the product of the two matrices (if possible).
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| 27. Compute the product of the two matrices (if possible).
If the product is not defined please enter undefined.
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| 28. Given , , and , which of the following can be calculated?
Can be calculated? __________ Can be calculated? __________ Can be calculated? __________ Can be calculated? __________
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| 29. Find the matrix product, if possible.
If the product is not defined please enter undefined.
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| 30. Translate the matrix equations into a system of linear equations.
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| 31. Translate the matrix equations into a system of linear equations.
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| 32. Translate the given system of equations into matrix form.
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| 33. Translate the system of equations into matrix form.
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34. Editors’ workloads were increasing during the 1990s, as the following table shows.
Write a matrix expression which would estimate the total number of books edited during the years 1993-1996.
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35. The chart shows the number of personal bankruptcy filings in three City regions during various months of 2001 – 2002.
Write a matrix product whose computation gives the total number by which bankruptcy filings in January, 2001, exceeded filings in January, 2002. Enter your answer in the form , where A is the matrix, B is the matrix, C is the matrix, and D is the matrix.
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| 1. Use the row reduction method to find the inverse, if it exists.
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| 2. Determine which pair of matrices is an inverse pair.
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| 3. Find the inverse of the given matrix, if it exists.
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| 4. Compute the determinant of the given matrix.
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| 5. Which of the following is a true statement?
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| 6. Use row reduction to find the inverse of the given matrix, if it exists. Check your answers by multiplication.
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| 7. Use row reduction to find the inverse of the given matrix, if it exists. Check your answer by multiplication.
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| 8. Use matrix inversion to solve the given system of linear equations.
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| 9. Use matrix inversion to solve the system of linear equations.
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| 10. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 11. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 12. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 13. Use matrix inversion to solve the given system of linear equations.
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| 14. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 15. Use matrix inversion to solve the given system of linear equations.
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| 16. Solve the system using the inverse matrix.
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| 17. Determine whether or not the pair of matrices is an inverse pair.
,
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| 18. Use the row reduction method to find the inverse of the matrix, if it exists.
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| 19. Compute the determinant of the matrix. If the determinant is nonzero, use the formula for inverting a matrix to calculate the inverse of the given matrix.
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| 20. Use matrix inversion to solve the system of linear equations.
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| 21. Solve the system using the inverse matrix.
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| 22. Use matrix inversion to solve the system of linear equations.
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| 23. Use matrix inversion to solve the given system of linear equations.
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| 24. Use matrix inversion to solve the given system of linear equations.
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| 25. Use matrix inversion to solve the given system of linear equations.
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| 26. Use the row reduction method to find the inverse, if it exists.
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| 27. Use the row reduction method to find the inverse of the given matrix, if it exists.
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| 28. Find the inverse of the given matrix, if it exists.
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| 29. Use matrix inversion to solve the given system of linear equations.
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| 30. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 31. Use row reduction to find the inverse of the given matrix, if it exists. Check your answer by multiplication.
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| 32. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 33. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 34. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 35. Use row reduction to find the inverse of the given matrix, if it exists, and check your answer by multiplication.
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| 36. Is the pair of matrices below the inverse pair?
,
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| 37. Is the following statement true or false?
If D and B are matrices and , then .
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| 38. Determine if the given pair of matrices is an inverse pair. Explain your work.
,
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| 1. Reduce the payoff matrix by dominance.
B p q r
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| 2. Reduce the payoff matrix by dominance.
B a b c
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| 3. Decide whether the game is strictly determined. If it is, give the players’ optimal pure strategies and the value of the game.
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| 4. Decide whether the game is strictly determined. If it is, give the players’ optimal pure strategies and the value of the game.
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| 5. Decide whether the game is strictly determined. If it is, give the players’ optimal pure strategies and the value of the game.
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| 6. Calculate the expected value of the game with the given payoff matrix using the mixed strategy supplied.
, ,
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| 7. For the given row strategy R, find the optimal pure strategy (or strategies) the other player should use. Express the answer as a row or column matrix.
,
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| 8. For the given row strategy R, find the optimal pure strategy (or strategies) the other player should use. Express the answer as a row or column matrix. Also determine the resulting expected value of the game.
,
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| 9. Find the optimal mixed row strategy, the optimal mixed column strategy, and the expected value of the game in the event that each player uses his or her optimal mixed strategy.
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| 10. Find the optimal mixed row strategy, the optimal mixed column strategy, and the expected value of the game in the event that each player uses his or her optimal mixed strategy.
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| 11. You and your friend have come up with the following simple game to pass the time: at each round, you simultaneously call “heads” or “tails”. If you have both called the same thing, your friend wins one point; if your calls differ, you win one point. Set up the payoff matrix.
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| 12. You are deciding whether to invade England, Sweden or Norway, and your opponent is simultaneously deciding which of these three countries to defend. If you invade a country that your opponent is defending, you will be defeated (payoff: -1), but if you invade a country your opponent is not defending, you will be successful (payoff: +1). Set up the payoff matrix.
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| 13. Your fast-food outlet, Burger Queen, has obtained a license to open branches in three closely situated South African cities: Brakpan, Nigel, and Springs. Your market surveys show that Brakpan and Nigel each provide a potential market of 2,500 burgers a day, while Springs provides a potential market of 1,000 burgers per day. Your company can only finance an outlet in one of those cities at the present time. Your main competitor, Burger Princess, has also obtained licenses for these cities, and is similarly planning to open only one outlet. If you both happen to locate at the same city, you will share the total business from all three cities equally, but if you locate in different cities, you will each get all the business in the cities in which you have located, plus half the business in the third city. The payoff is the number of burgers you will sell per day minus the number of burgers your competitor will sell per day. Set up the payoff matrix.
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| 14. When you bet on a racehorse with odds of m-n, you stand to win m dollars for every bet of n dollars if your horse wins; for instance, if the horse you bet on is running at 5-2 and wins, you will win $5 for every $2 you bet. (Thus a $2 bet will return $7.). Here are some actual odds from a 1992 race at Belmont Park, NY. The favorite at 5-1 was Pleasant Tap. The second choice was Thunder Rumble at 7-2, while the third choice was Strike the Gold at 4-1. Assume you are making a $30 bet on one of these horses. The payoffs are your winnings. (If your horse does not win, you lose your entire bet. Of course, it is possible for none of your horses to win.) Suppose that just before the race, there has been frantic betting on Thunder Rumble, with the result that the odds have dropped to 2-5. The odds on the other two horses remain unchanged. Set up the payoff matrix.
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| 15. City Community College (CCC) plans to host Midtown Military Academy (MMA) for a wrestling tournament. Each school has three wrestlers in the 190 lb. weight class: CCC has Pablo, Sal, and Edison, while MMA has Carlos, Marcus and Noto. Pablo can beat Carlos and Marcus, Marcus can beat Sal and Edison, Sal can beat Carlos, Noto can beat Edison, while the other combinations will result in an even match. Set up a payoff matrix, and use reduction by dominance to decide which wrestler each team should choose as their champion. Does one school have an advantage over the other?
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16. In the Second World War, during the struggle for New Guinea, intelligence reports revealed that the Japanese were planning to move a troop and supply convoy from the port of Rabaul at the Eastern tip of New Britain to Lae, which lies just west of New Britain on New Guinea. It could either travel via a northern route which was plagued by poor visibility, or by a southern route, where the visibility was clear. General Kenney, who was the commander of the Allied Air Forces in the area, had the choice of concentrating reconnaissance aircraft on one route or the other, and bombing the Japanese convoy once it was sighted. Suppose that General Kenney had a third alternative: Splitting his reconnaissance aircraft between the two routes Kenney’s staff drafted the following outcomes for his choices, where the payoffs are estimated days of bombing time:
What would you have recommended to General Kenney? What would you have recommended to the Japanese Commander? How much bombing time results if these recommendations are followed?
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| 17. Florida and Ohio are “swing states” that have a large bounty of electoral votes and are therefore highly valued by presidential campaign strategists. Suppose it is now the weekend before Election Day 2004, and each candidate (Bush and Kerry) can visit only one more state. Further, to win the election, Bush needs to win both of these states. Currently Bush has a 70% chance of winning Ohio and a 30% chance of winning Florida. Therefore, he has a 0.70×0.30 = 0.21, or 21% chance of winning the election. Assume that each candidate can increase his probability of winning a state by 20% if he, and not his opponent, visits that state. If both candidates visit the same state, there is no effect. Set up a payoff matrix with Bush as the row player and Kerry as the column player, where the payoff for a specific set of circumstances is the probability (expressed as a percentage) that Bush will win both states.
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| 18. Your Abercrom B men’s fashion outlet has a 40% chance of launching an expensive new line of used auto-mechanic dungarees (complete with grease stains) and a 60% chance of staying instead with its traditional torn military-style dungarees. Your rival across from you in the mall, Abercrom A, appears to be deciding between a line of torn gym shirts and a more daring line of “empty shirts” (that is, empty shirt boxes). Your corporate spies reveal that there is a 40% chance that Abercrom A will opt for the empty shirt option. The payoff matrix gives the number of customers your outlet can expect to gain from Abercrom A in each situation.
Abercrom A Torn Empty Shirts Shirts Abercrom B What is the expected resulting effect on your customer base? Round the answer to the nearest whole number.
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19. A manufacturer of electrical machinery is located in a cramped, though low-rent, factory close to the center of a large city. The firm needs to expand, and it could do so in one of three ways: (1) remain where it is and install new equipment, (2) move to a suburban site in the same city, or (3) relocate in a different part of the country where labor is cheaper. Its decision will be influenced by the fact that one of the following will happen: (I) the government may introduce a program of equipment grants, (II) a new suburban highway may be built, or (III) the government may institute a policy of financial help to companies who move into regions of high unemployment. The value to the company of each combination is given in the following payoff matrix.
If the manufacturer judges that there is a 60% probability that the government will go with option I, a 30% probability that they will go with option II, and a 10% probability that they will go with option III, what is the manufacturer’s best option?
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20. A farmer has a choice of growing wheat, barley, or rice. Her success will depend on the weather, which could be dry, average, or wet. Her payoff matrix is as follows.
If the probability that the weather will be dry is 50%, the probability that it will be average is 10%, and the probability that it will be wet is 40%, what is the farmer’s best choice of crop?
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| 21. Your Abercrom B men’s fashion outlet has a 60% chance of launching an expensive new line of used auto-mechanic dungarees (complete with grease stains) and a 40% chance of staying instead with its traditional torn military-style dungarees. Your rival across from you in the mall, Abercrom A, appears to be deciding between a line of torn gym shirts and a more daring line of “empty shirts” (that is, empty shirt boxes). Your corporate spies reveal that there is a 50% chance that Abercrom A will opt for the empty shirt option. The payoff matrix gives the number of customers your outlet can expect to gain from Abercrom A in each situation.
Abercrom A Torn Empty Shirts Shirts Abercrom B How many customers can you expect to lose? Round the answer to the nearest whole. __________ customers
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| 22. Reduce the payoff matrix by dominance.
B p q r
A
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| 23. Reduce the payoff matrix by dominance.
B a b c
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| 24. Decide whether the game is strictly determined.
B p q __________ (strictly determined or not strictly determined) If it is, what are the players’ optimal pure strategies?
What is the value of the game? __________
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| 25. Decide whether the game is strictly determined.
B p q r __________ (answer strictly determined or not strictly determined) If it is, what are the players’ optimal pure strategies?
What is the value of the game? __________
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| 26. Decide whether the game is strictly determined.
B a b c __________ (answer strictly determined or not strictly determined) If it is, what are the players’ optimal pure strategies?
What is the value of the game? __________
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27. You and your friend have come up with the following simple game to pass the time: at each round, you simultaneously call “heads” or “tails”. If you have both called the same thing, your friend wins one point; if your calls differ, you win one point. Set up the payoff matrix with you as the row player and your friend as the column player.
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28. You are deciding whether to invade Japan, Sweden or Canada, and your opponent is simultaneously deciding which of these three countries to defend. If you invade a country that your opponent is defending, you will be defeated (payoff: -2), but if you invade a country your opponent is not defending, you will be successful (payoff: +2). Set up the payoff matrix with you as the row player and your opponent as the column player.
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| 29. Your fast-food outlet, Burger Queen, has obtained a license to open branches in three closely situated South African cities: Brakpan, Nigel, and Springs. Your market surveys show that Brakpan and Nigel each provide a potential market of 2,500 burgers a day, while Springs provides a potential market of 1,000 burgers per day. Your company can only finance an outlet in one of those cities at the present time. Your main competitor, Burger Princess, has also obtained licenses for these cities, and is similarly planning to open only one outlet. If you both happen to locate at the same city, you will share the total business from all three cities equally, but if you locate in different cities, you will each get all the business in the cities in which you have located, plus half the business in the third city. The payoff is the number of burgers you will sell per day minus the number of burgers your competitor will sell per day. Set up the payoff matrix with you as the row player and your opponent as the column player.
Let the first column correspond to Brakpan, the second one to Nigel, the third one to Springs and the first row correspond to the Brakpan, the second one to the Nigel, the third one to Springs.
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| 30. When you bet on a racehorse with odds of m-n, you stand to win m dollars for every bet of n dollars if your horse wins; for instance, if the horse you bet is running at 5-2 and wins, you will win $5 for every $2 you bet. (Thus a $2 bet will return $7.). Here are some actual odds from a 1992 race at Belmont Park, NY. The favorite at 4-1 was Pleasant Tap. The second choice was Thunder Rumble at 7-2, while the third choice was Strike the Gold at 7-2. Assume you are making a $20 bet on one of these horses. The payoffs are your winnings. (If your horse does not win, you lose your entire bet. Of course, it is possible for none of your horses to win.) Suppose that just before the race, there has been frantic betting on Thunder Rumble, with the result that the odds have dropped to 1-5. The odds on the other two horses remain unchanged. Set up the payoff matrix with your bet as the row player and winner as the column player.
Let the first column correspond to Pleasant Tap, the second one to Thunder Rumble, the third one to Strike the Gold and the first row correspond to Pleasant Tap, the second one to Thunder Rumble, the third one to Strike the Gold .
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31. In the Second World War, during the struggle for New Guinea, intelligence reports revealed that the Japanese were planning to move a troop and supply convoy from the port of Rabaul at the Eastern tip of New Britain to Lae, which lies just west of New Britain on New Guinea. It could either travel via a northern route which was plagued by poor visibility, or by a southern route, where the visibility was clear. General Kenney, who was the commander of the Allied Air Forces in the area, had the choice of concentrating reconnaissance aircraft on one route or the other, and bombing the Japanese convoy once it was sighted. Suppose that General Kenney had a third alternative: Splitting his reconnaissance aircraft between the two routes Kenney’s staff drafted the following outcomes for his choices, where the payoffs are estimated days of bombing time:
What would you have recommended to General Kenney? __________ (Northern Route or Split Reconnaissance or Southern Route) What would you have recommended to the Japanese Commander? __________ (Northern Route or Southern Route) How much bombing time results if these recommendations are followed? __________days
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| 32. Calculate the expected value of the game with the given payoff matrix using the mixed strategy supplied.
, ,
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33. A manufacturer of electrical machinery is located in a cramped, though low-rent, factory close to the center of a large city. The firm needs to expand, and it could do so in one of three ways: (1) remain where it is and install new equipment, (2) move to a suburban site in the same city, or (3) relocate in a different part of the country where labor is cheaper. Its decision will be influenced by the fact that one of the following will happen: (I) the government may introduce a program of equipment grants, (II) a new suburban highway may be built, or (III) the government may institute a policy of financial help to companies who move into regions of high unemployment. The value to the company of each combination is given in the following payoff matrix.
If the manufacturer judges that there is a 10% probability that the government will go with option I, a 10% probability that they will go with option II, and a 80% probability that they will go with option III, what is the manufacturer’s best option?
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34. A farmer has a choice of growing wheat, barley, or rice. Her success will depend on the weather, which could be dry, average, or wet. Her payoff matrix is as follows.
If the probability that the weather will be dry is 20%, the probability that it will be average is 60%, and the probability that it will be wet is 20%, what is the farmer’s best choice of crop?
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| 1. Each unit of television news requires 1.1 units of television news and 0.1 units of radio news. Each unit of radio news requires 0.3 units of television news and no radio news. With sector 1 as television news and sector 2 as radio news, set up the technology matrix A .
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| 2. Let A be the technology matrix, where Sector 1 is paper, and Sector 2 is wood.
How many units of wood are needed to produce one unit of paper? How many units of paper are needed to produce one unit of paper? How many units of paper are needed to produce one unit of wood?
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| 3. Let A be the technology matrix, where Sector 1 is computer chips, and Sector 2 is silicon.
How many units of computer chips are needed to produce one unit of silicon? How many units of silicon are needed to produce one unit of silicon? How many units of silicon are needed to produce one unit of computer chips ?
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| 4. Production of 1 unit of cologne requires 0.9 units of perfume and 0.4 units of cologne. Into 1 unit of perfume goes 0.2 unit of perfume and 0.5 units of cologne. With sector 1 as cologne and sector 2 as perfume, set up the technology matrix A.
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| 5. Given the technology matrix A, and an external demand vector D, find the production vector X.
,
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| 6. Given the technology matrix A, and an external demand vector D, find the production vector X.
,
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| 7. Given the technology matrix A, and an external demand vector D, find the production vector X. Round your answer to one decimal places.
,
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| 8. Given the technology matrix A, and an external demand vector D, find the production vector X.
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| 9. Let and assume that the external demand for the products in Sector 1 increases by 1 unit. By how many units should each sector increase production?
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| 10. Let and assume that the external demand for the products in each of the sectors increases by 1 unit. By how many units should each sector increase production?
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11. Obtain the technology matrix from the input-output table.
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12. Two student groups at Enormous State University, the Choral Society and the Football Club, maintain files of term papers that they write and offer to students for research purposes. Some of these papers they use themselves in generating more papers. To avoid suspicion of plagiarism by faculty members (who seem to have astute memories), each paper is given to students or used by the clubs only once (no copies are kept). The number of papers that were used in the production of new papers last year is shown in the input-output table below.
Given that 990 Choral Society papers and 1,485 Football Club papers will be used by students outside of these two clubs next year, how many new papers do the two clubs need to write?
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13. Two sectors of any country economy are (1) audio, video, and communication equipment and (2) electronic components and accessories. In 1998, the input-output table involving these two sectors was as follows (all figures are in millions of dollars):
Determine the production levels necessary in these two sectors to meet an external demand for $60,000 million of communication equipment and $90,000 million of electronic components. Round answers to two significant digits.
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14. Two sectors of any country economy are (1) lumber and wood products and (2) paper and allied products. In 1998 the input-output table involving these two sectors was as follows (all figures are in millions of dollars).
If external demand for lumber and wood products rises by $14,000 million and external demand for paper and allied products rises by $22,000 million, what increase in output of these two sectors is necessary? Round answers to two significant digits.
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| 15. Two sectors of some economy are Sector 1 and Sector 2. The input-output table involving these two sectors results in the following value for
How many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 1?
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| 16. Two sectors of some economy are Sector 1 and Sector 2. The input-output table involving these two sectors results in the following value for
How many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 2?
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17. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars)
Determine how these four sectors would react to an increase in demand for Sector 1 production of $1,000 million.
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18. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars)
Determine how these four sectors would react to an increase in demand for Sector 1 production of $1000 million.
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19. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars)
How much additional production by the Sector 3 is necessary to accommodate a $100 increase in the demand for the products of Sector 1?
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20. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars):
How much additional production by the Sector 1 is necessary to accommodate a $1,000 increase in the demand for the products of Sector 4? Please round your answer to two decimal places.
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| 21. Two sectors of some economy are Sector 1 and Sector 2. The input-output table involving these two sectors results in the following value for
How many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 1? Round your answer to three decimal places.
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| 22. Two sectors of some economy are Sector 1 and Sector 2. The input-output table involving these two sectors results in the following value for
How many additional dollars worth of production of Sector 2 must be produced to meet a $1 increase in the demand for products of Sector 2? Round your answer to four decimal places.
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23. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars)
How much additional production by the Sector 3 is necessary to accommodate a $100 increase in the demand for the products of Sector 1? Round your answers to two decimal places. $ __________
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24. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars):
How much additional production by the Sector 1 is necessary to accommodate a $1,000 increase in the demand for the products of Sector 4? Round your answer to two decimal places. $ __________ million
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| 25. Given the technology matrix A, and an external demand vector D, find the production vector X.
,
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| 26. Given the technology matrix A, and an external demand vector B, find the production vector X.
,
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| 27. Given the technology matrix A, and an external demand vector D, find the production vector X.
,
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28. Obtain the technology matrix from the following input-output table.
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| 29. Let A be the technology matrix, where Sector 1 = wood, and Sector 2 = paper.
__________ units of paper are needed to produce one unit of wood. __________ units of wood are needed to produce one unit of paper. The production of each unit of paper requires the use of __________ units of paper.
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30. Production of 1 unit of cologne requires 0.7 units of perfume and 0.3 units of cologne. Into 1 unit of perfume goes 0.2 unit of perfume and 0.4 units of cologne. With sector 1 as cologne and sector 2 as perfume, set up the technology matrix A.
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31. Each unit of television news requires 0.5 units of television news and 0.4 units of radio news. Each unit of radio news requires 0.7 units of television news and no radio news. With sector 1 as television news and sector 2 as radio news, set up the technology matrix A.
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| 32. Given the technology matrix A, and an external demand vector D, find the production vector X.
,
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| 33. Let and assume that the external demand for the products in Sector 1 increases by 1 unit. By how many units should each sector increase production?
Express the answer as a column matrix.
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34. Let and assume that the external demand for the products in each of the sectors increases by 1 unit. By how many units should each sector increase production?
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35. Two student groups at Enormous State University, the Choral Society and the Football Club, maintain files of term papers that they write and offer to students for research purposes. Some of these papers they use themselves in generating more papers. To avoid suspicion of plagiarism by faculty members (who seem to have astute memories), each paper is given to students or used by the clubs only once (no copies are kept). The number of papers that were used in the production of new papers last year is shown in the input-output table below.
Given that 110 Choral Society papers and 330 Football Club papers will be used by students outside of these two clubs next year, how many new papers do the two clubs need to write? Choral Society __________, Football Club __________
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36. Two sectors of any country economy are (1) audio, video, and communication equipment and (2) electronic components and accessories. In 1998, the input-output table involving these two sectors was as follows (all figures are in millions of dollars):
Determine the production levels necessary in these two sectors to meet an external demand for $80,000 million of communication equipment and $110,000 million of electronic components. Round answers to two significant digits. Equipment Sector production approximately __________ million, Components Sector production approximately __________ million.
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37. Two sectors of any country economy are (1) lumber and wood products and (2) paper and allied products. In 1998 the input-output table involving these two sectors was as follows (all figures are in millions of dollars).
If external demand for lumber and wood products rises by $10,000 million and external demand for paper and allied products rises by $9,000 million, what increase in output of these two sectors is necessary? Round answers to two significant digits.
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38. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars)
Determine how these four sectors would react to an increase in demand for Sector 1 production of $1,000 million. Round your answers to two decimal places. Express the answer as a column matrix.
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39. Four sectors of some economy are (1) Sector 1, (2) Sector 2, (3) Sector 3, and (4) Sector 4. The input-output table involving these four sectors was as follows (all figures are in millions of dollars)
Determine how these four sectors would react to an increase in demand for Sector 1 production of $1,000 million. Round your answers to two decimal places. Express the answer as a column matrix.
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| 40. True or False?
Let be the technology matrix, be the production vector, and be the external demand vector. There would be 0.4 units of sector 2 needed to produce one unit of sector 2.
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Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
