College Algebra with Applications for Business and Life Sciences 2nd Edition by Ron Larson - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Determine which ordered pair is a solution of the system. A) (2, –5) B) (5, 2) …
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College Algebra with Applications for Business and Life Sciences 2nd Edition by Ron Larson – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
| 1. | Determine which ordered pair is a solution of the system.
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| A) | (2, –5) | |
| B) | (5, 2) | |
| C) | (–3, 2) | |
| D) | (–5, 2) | |
| E) | (–2, –3) | |
| Ans: | D | |
| 2. | Determine which ordered pair is a solution of the system.
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| A) | ||
| B) | ||
| C) | (–9, 86) | |
| D) | ||
| E) | (–9, 17) | |
| Ans: | D | |
| 3. | Determine which ordered pair is a solution of the system.
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| A) | (–4, –2) | |
| B) | (–8, 9) | |
| C) | (–8, –1) | |
| D) | (–2, 4) | |
| E) | (–4, 2) | |
| Ans: | A | |
| 4. | Solve each system of equations by the substitution method.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | no solution | |
| Ans: | C | |
| 5. | Solve the system by the method of substitution.
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| A) | (–2, 1) | |
| B) | (–1, –2) | |
| C) | (1, –2) | |
| D) | (–2, –1) | |
| E) | (2, 1) | |
| Ans: | D | |
| 6. | Solve the system by the method of substitution.
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| A) | (2, 1), (–1, –2) | |
| B) | (2, 3), (–1, 0) | |
| C) | (2, –1), (–1, –4) | |
| D) | (2, –1) | |
| E) | no real solution | |
| Ans: | B | |
| 7. | Solve the system of equations below.
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| A) | and | |
| B) | and | |
| C) | and | |
| D) | and | |
| E) | and | |
| Ans: | B | |
| 8. | Solve the system by the method of substitution.
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| A) | (12, 5), (–12, –5) | |
| B) | (12, 5) | |
| C) | (12, 5), (–12, 5), (–12, –5), (12, –5) | |
| D) | (5, 12), (5, –12) | |
| E) | no real solution | |
| Ans: | A | |
| 9. | Solve the system below by method of substitution, if possible.
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| A) | no solution | |
| B) | ||
| C) | ||
| D) | , | |
| E) | ||
| Ans: | A | |
| 10. | Solve the system by the method of substitution.
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| A) | (–3, 48), (4, –29), (1, –8) | |
| B) | (–3, 48), (–1, 16) | |
| C) | (–4, 67), (1, –8) | |
| D) | (–3, 48), (–4, 67), (0, 3) | |
| E) | no real solution | |
| Ans: | D | |
| 11. | Solve the system graphically.
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| B) |
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| Ans: | C | |
| 12. | Determine whether the system of equations below has one solution, two solutions, or no solution.
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| A) | two solutions | |
| B) | no solution | |
| C) | one solution | |
| Ans: | B | |
| 13. | Solve the system of equations below by the substitution method.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | no solution | |
| Ans: | E | |
| 14. | Use a graphing utility to find the point(s) of intersection of the graphs.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | ||
| Ans: | C | |
| 15. | Find the sales necessary to break even (R – C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)
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| A) | 666 units | |
| B) | 666 units or 714 units | |
| C) | 714 units | |
| D) | 698 units | |
| E) | no real solution | |
| Ans: | C | |
| 16. | You invest $3700 in a fishing lure business. A lure costs $1.60 to produce and will be sold for $6.20. How many lures must you sell to break even? | |
| A) | 1716 lures | |
| B) | 805 lures | |
| C) | 2313 lures | |
| D) | 475 lures | |
| E) | 597 lures | |
| Ans: | B | |
| 17. | The sales of various types of lawn and garden items vary according to the season. At a certain home improvement store, the monthly sales H of garden hoses (hoses sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval. The sales of these two items during the calendar months July-October are modeled by the equations:
H(t) = 64 – 6t R(t) = 17t – 97, where t is the month (t = 7 corresponds to July). In which month does the number of rakes sold equal the number of hoses sold? |
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| A) | August | |
| B) | September | |
| C) | October | |
| D) | November | |
| E) | July | |
| Ans: | E | |
| 18. | A total of $50,000 is invested in two funds paying 6.5% and 7.5% simple interest. The total yearly interest is $3600. How much is invested at the 6.5% rate? | |
| A) | $28,000 | |
| B) | $12,000 | |
| C) | $26,000 | |
| D) | $15,000 | |
| E) | $20,000 | |
| Ans: | D | |
| 19. | You are offered two different jobs. Company A offers an annual salary of $34,000 plus a year-end bonus of 3.5% of your total sales. Company B offers a salary of $28,000 plus a year-end bonus of 7.5% of your total sales. What is the amount you must sell in one year to earn the same salary working for either company? | |
| A) | $170,000 | |
| B) | $120,000 | |
| C) | $150,000 | |
| D) | $90,000 | |
| E) | $130,000 | |
| Ans: | C | |
| 20. | Solve the system by the method of elimination.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | B | |
| 21. | Solve the system by elimination.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | C | |
| 22. | Solve each system of equations by the elimination method.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | no solution | |
| Ans: | A | |
| 23. | Solve the system below by elimination if possible. Then state whether the system below is consistent or inconsistent.
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| A) | The system is consistent and its solution is | |
| B) | The system is consistent and its solution is | |
| C) | The system is consistent and its solution is | |
| D) | The system is consistent and its solution is | |
| E) | The system is inconsistent and no solution exists. | |
| Ans: | E | |
| 24. | Solve the system by the method of elimination.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | D | |
| 25. | Solve the system by the method of elimination.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | C | |
| 26. | Use the statements below to write a system of equations. Solve the system by elimination.
The sum of twice a number and a number is –14. The difference of and is 2. |
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | ||
| Ans: | D | |
| 27. | An airplane flying into a headwind travels 280 miles in 2 hours and 48 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant. | |
| A) | plane speed = 135 mph; wind speed = 27 mph | |
| B) | plane speed = 135 mph; wind speed = 20 mph | |
| C) | plane speed = 97 mph; wind speed = 9 mph | |
| D) | plane speed = 97 mph; wind speed = 20 mph | |
| E) | plane speed = 120 mph; wind speed = 20 mph | |
| Ans: | E | |
| 28. | One acetic acid solution is 60% water and another is 40% water. How many liters of each solution should be mixed to produce 20 liters of a solution that is 49% water? | |
| A) | 5 liters of the 60% solution and 15 liters of the 40% solution | |
| B) | 9 liters of the 60% solution and 11 liters of the 40% solution | |
| C) | 15 liters of the 60% solution and 5 liters of the 40% solution | |
| D) | 6 liters of the 60% solution and 14 liters of the 40% solution | |
| E) | 14 liters of the 60% solution and 6 liters of the 40% solution | |
| Ans: | B | |
| 29. | A total of $28,000 is invested in two corporate bonds that pay 11% and 4% simple interest. The total annual interest is $2170. How much is invested in the 4% bond? | |
| A) | $17,000 | |
| B) | $15,000 | |
| C) | $13,000 | |
| D) | $18,000 | |
| E) | $16,000 | |
| Ans: | C | |
| 30. | Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.)
Demand Supply p = 36 – 0.02x p = 0.5x – 380 |
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | A | |
| 31. | The supply and demand equations for a small LCD television are given by
where is the price (in dollars) and represents the number of televisions. For how many units will the quantity demanded equal the quantity supplied? What price corresponds to this value? |
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| A) | 1855 units at $463.75 | |
| B) | 2230 units at $257.50 | |
| C) | 1480 units at $257.50 | |
| D) | 2230 units at $670.00 | |
| E) | 1480 units at $670.00 | |
| Ans: | E | |
| 32. | Find the least squares regression line y = ax + b for the points
by solving the system for a and b.
Points: space |
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| A) | y = 1.92x – 2.92 | |
| B) | y = –0.15x + 1.92 | |
| C) | y = –2.53x + 1.63 | |
| D) | y = –2.92x + 1.92 | |
| E) | y = 1.19x + 1.63 | |
| Ans: | D | |
| 33. | The concentration (in parts per million) of carbon dioxide in the atmosphere is measured at the Mauna Loa Observatory in Hawaii. The greatest monthly carbon dioxide concentration for each year from 2002 to 2006 is shown in the table.
Solve the following system for and to find the least squares regression line for the data. Let represent the year, with corresponding to 2002.
Use the least square regression line to predict the largest monthly carbon dioxide concentration in 2014. Round your answer to the nearest hundredths part per million. |
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| A) | 396.20 parts per million | |
| B) | 400.73 parts per million | |
| C) | 389.40 parts per million | |
| D) | 398.46 parts per million | |
| E) | 402.99 parts per million | |
| Ans: | E | |
| 34. | Determine which one of the ordered triples below is a solution of the given system of equations. | |
| A) | (7, 5, 17) | |
| B) | (–3, –2, 6) | |
| C) | (–2, –6, 3) | |
| D) | (7, 5, 6) | |
| E) | (6, –2, –3) | |
| Ans: | B | |
| 35. | Determine which of the following systems of equations is in row-echelon form.
System I:
System II:
System III: |
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| A) | None of the systems are in row-echelon form. | |
| B) | Only system II is in row-echelon form. | |
| C) | Only systems II and III are in row-echelon form. | |
| D) | All systems are in row-echelon form. | |
| E) | Only systems I and III are in row-echelon form. | |
| Ans: | C | |
| 36. | Use back-substitution to solve the system of linear equations.
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| B) | ||
| C) | ||
| D) | ||
| E) | ||
| Ans: | B | |
| 37. | Solve the system of linear equations.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | B | |
| 38. | Solve the system of equations below, if possible.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | The system is inconsistent. | |
| Ans: | E | |
| 39. | Solve the system of linear equations.
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| C) | ||
| D) | ||
| E) | ||
| Ans: | C | |
| 40. | Solve the system of linear equations.
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| B) | ||
| C) | ||
| D) | ||
| E) | ||
| Ans: | B | |
| 41. | Solve the system of equations below:
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| B) | ||
| C) | ||
| D) | ||
| E) | ||
| Ans: | C | |
| 42. | Solve the system of equations below:
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| Ans: | E | |
| 43. | Solve the system of equations below:
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| E) | ||
| Ans: | B | |
| 44. | Solve the system of linear equations.
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| A) | ||
| B) | ||
| C) | ||
| D) | ||
| E) | inconsistent | |
| Ans: | D | |
| 45. | Which of the following systems of equations has as a solution the ordered triple
System I:
System II:
System III: |
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| A) | Only system II has the ordered triple as a solution. | |
| B) | Only systems I and II have the ordered triple as a solution. | |
| C) | Each of the systems I, II, and III has the ordered triple as a solution. | |
| D) | Only system III has the ordered triple as a solution. | |
| E) | None of the systems has the ordered triple as a solution. | |
| Ans: | B | |
| 46. | Which of the following three ordered triples are of the given form below.
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| A) | Only triple I and II are in the given form. | |||||||
| B) | None of the triples are in the given form. | |||||||
| C) | Only triple I and III are in the given form. | |||||||
| D) | Only triple III is in the given form. | |||||||
| E) | Only triple II is in the given form. | |||||||
| Ans: | E | |||||||
| 47. | Find an equation of the form whose graph passes through the points and | |
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| Ans: | A | |
| 48. | Find the equation of the parabolathat passes through the points.
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| Ans: | E | |
| 49. | Find the equation of the circle
that passes through the points . |
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| Ans: | A | |
| 50. | A real estate company borrows $2,000,000. Some of the money is borrowed at 4%, some at 8%, and some at 11% simple annual interest. How much is borrowed at the 11% rate when the total annual interest is $130,000 and the amount borrowed at 4% is the same as the amount borrowed at 8%? | |
| A) | $500,000 | |
| B) | $200,000 | |
| C) | $300,000 | |
| D) | $600,000 | |
| E) | $900,000 | |
| Ans: | B | |
| 51. | A mixture of 5 gallons of chemical A, 6 gallons of chemical B, and 22 gallons of chemical C is required to kill a crop destroying insect. Commercial spray X contains 1, 2, and 3 parts of these chemicals, respectively. Commercial spray Y contains only chemical C. Commercial spray Z contains chemicals A, B, and C in equal amounts. How much of commercial spray is needed to obtain the desired mixture? | |
| A) | 2 gallons | |
| B) | 3 gallons | |
| C) | 1 gallon | |
| D) | 6 gallons | |
| E) | 15 gallons | |
| Ans: | D | |
| 52. | A chemist needs 20 liters of a 45% acid solution. The solution is to be mixed from three solutions whose acid concentrations are 10%, 20%, and 50%. How many liters of the 50% solution should the chemist use if trying to use as little as possible of the 50% solution? | |
| A) | liters | |
| B) | liters | |
| C) | liters | |
| D) | liters | |
| E) | liters | |
| Ans: | C | |
| 53. | A residential building contractor borrowed $31,000 to complete a new home. Some of the money was borrowed at 5%, some at 7%, and some at 9%. How much was borrowed at each rate if the annual interest owed was $2050 and the amount borrowed at 7% is three times more than the amount borrowed at 9%? | |
| A) | $9000 at 5%; $17,000 at 7%; $5000 at 9% | |
| B) | $11,000 at 5%; $15,000 at 7%; $5000 at 9% | |
| C) | $9000 at 5%; $16,000 at 7%; $6000 at 9% | |
| D) | $10,000 at 5%; $13,000 at 7%; $7000 at 9% | |
| E) | $9000 at 5%; $18,000 at 7%; $6000 at 9% | |
| Ans: | B | |
| 54. | The federal debt of the United States as a percentage of the Gross Domestic Product (GDP) from 2001 to 2005 is shown in the table. In the table, represents the year, with corresponding to 2002.
Find the least squares regression parabola for the data by solving the following system.
Use the model to predict the federal debt as percents of GDP in 2010. Round to the nearest tenth percents. |
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| A) | 64.2% | |
| B) | 52.7% | |
| C) | 56.5% | |
| D) | 61.9% | |
| E) | 48.2% | |
| Ans: | C | |
| 55. | Write an inequality for the shaded region shown in the figure. | |
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| Ans: | E | |
| 56. | Sketch the graph of the inequality below.
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| 57. | Sketch the graph of the inequality below.
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| 58. | Sketch the graph of the inequality below.
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| 59. | Use a graphing utility to graph the inequality. Shade the region representing the solution.
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| Ans: | B | |
| 60. | Graph the solution set of the system of inequalities below.
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| 61. | Sketch the graph of the solution set of each system of inequalities.
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| 62. | Sketch the graph and label the vertices of the solution set of the system of inequalities. Shade the solution set.
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| Ans: | E | |
| 63. | Sketch the graph of the solution set of each system of inequalities.
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| 64. | Graph the solution set of the system of inequalities below.
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| 65. | Write a system of inequalities whose solution set is graphed below.
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| Ans: | A | |
| 66. | Derive a set of inequalities to describe the region.
Triangle: vertices at (0, 0), (5, 0), (5, 4) |
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| Ans: | A | |
| 67. | A furniture company produces tables and chairs. Each table requires 1 hour in the assembly center and 2.25 hours in the finishing center. Each chair requires 0.75 hour in the assembly center and 0.5 hour in the finishing center. The company’s assembly center is available 18 hours per day, and its finishing center is available 12 hours per day. Let and be the number of tables and chairs produced per day, respectively. Find a system of inequalities describing all possible production levels. | |
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| Ans: | E | |
| 68. | For the given supply and demand equations, find the consumer surplus. Round to the nearest dollar.
Demand Supply p = 170 – 0.00003x p = 140 + 0.00004x |
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| A) | $2,755,102 | |
| B) | $3,030,612 | |
| C) | $3,306,122 | |
| D) | $4,132,653 | |
| E) | $3,673,469 | |
| Ans: | A | |
| 69. | Find the consumer surplus for the pair of demand and supply equations below.
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| A) | $1,250,000 | |
| B) | $3,750,000 | |
| C) | $5,000,000 | |
| D) | $2,500,000 | |
| E) | $1,875,000 | |
| Ans: | B | |
| 70. | You plan to invest up to $30,000 in two different interest-bearing accounts. Each account is to contain at least $9000. Moreover, one account should have at least three times the amount that is in the other account. Find a system of inequalities that describes the amount that you can invest in each account. | |
| A) | ||
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| Ans: | D | |
| 71. | A dietitian designs a special diet supplement using two different foods. Each ounce of food X contains 10 units of calcium, 15 units of iron, and 20 units of vitamin B. Each ounce of food Y contains 15 units of calcium, 10 units of iron, and 20 units of vitamin B. The minimum daily requirements for the diet are 380 units of calcium, 240 units of iron, and 390 units of vitamin B. Which combinations of foods X and Y below, if any, can be given to the patient to meet the minimum daily requirements?
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| A) | Only combinations II and III meet the minimum daily requirement. | |||||||
| B) | Only combination II meets the minimum daily requirement. | |||||||
| C) | None of the combinations meet the minimum daily requirement. | |||||||
| D) | Only combinations I and II meet the minimum daily requirement. | |||||||
| E) | Only combination III meets the minimum daily requirement. | |||||||
| Ans: | D | |||||||
| 72. | Find which of the following system of inequalities has a right triangle as a graphed solution set.
System I:
System II:
System III: |
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| A) | No systems have a right triangle as a graphed solution set. | |
| B) | Only systems II and III have a right triangle as a graphed solution set. | |
| C) | Only systems I and III have a right triangle as a graphed solution set. | |
| D) | Only system I has a right triangle as a graphed solution set. | |
| E) | Only systems I and II have a right triangle as a graphed solution set. | |
| Ans: | B | |
| 73. | Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints.
Objective function:
Constraints:
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| Ans: | E | |
| 74. | Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.)
Objective function:
Constraints:
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| Ans: | B | |
| 75. | Which of the following vertices of the constraint region shown is a maximum value of the objective function below.
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| A) | only vertex C | |
| B) | vertices A and D | |
| C) | vertices B and C | |
| D) | only vertex D | |
| E) | only vertex B | |
| Ans: | E | |
| 76. | Which of the following vertices of the constraint region shown is a minimum value of the objective function below.
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|
| A) | vertices C and D | |
| B) | only vertex C | |
| C) | only vertex A | |
| D) | vertices B and C | |
| E) | only vertex D | |
| Ans: | B | |
| 77. | An ice cream supplier has two machines that produce vanilla and chocolate ice cream. To meet one of its contractual obligations, the company must produce at least 11 gallons of vanilla ice cream and 90 gallons of chocolate ice cream per day. One machine makes 5 gallons of vanilla and 6 gallons of chocolate ice cream per hour. The second machine makes 1 gallons of vanilla and 14 gallons of chocolate ice cream per hour. It costs $21 per hour to run machine 1 and $26 per hour to run machine 2. How many hours should each machine be operated to fulfill the contract at the least expense? | |
| A) | Machine 1 for 6 hours and machine 2 for 1 hour. | |
| B) | Machine 1 for 1 hour and machine 2 for no hours. | |
| C) | Machine 1 for 1 hour and machine 2 for 6 hours. | |
| D) | Machine 1 for 6 hours and machine 2 for no hours. | |
| E) | Machine 1 for no hours and machine 2 for 1 hour. | |
| Ans: | C | |
| 78. | A company has budgeted a maximum of $1,200,000 for national advertising an allergy medication. Each minute of television time costs $120,000 and each one-page newspaper ad costs $60,000. Each television ad is expected to be viewed by 24 million viewers, and each newspaper ad is expected to be seen by 7 million readers. What is the optimal amount that should be spent on advertising for each type ad? | |
| A) | $1,200,000 on television time and $0 on newspaper ads | |
| B) | $1,000,000 on television time and $200,000 on newspaper ads | |
| C) | $500,000 on television time and $700,000 on newspaper ads | |
| D) | $600,000 on television time and $600,000 on newspaper ads | |
| E) | $900,000 on television time and $300,000 on newspaper ads | |
| Ans: | A | |
| 79. | An investor has $300,000 to invest in two types of investments. Type A pays 5% annually and type B pays 7% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-third of the total portfolio is to be allocated to type A investments and at least one-third of the portfolio is to be allocated to type B investments. What is the optimal amount that should be invested in each investment? | |
| A) | $100,000 in type A (5%), $200,000 in type B (7%) | |
| B) | $0 in type A (5%), $300,000 in type B (7%) | |
| C) | $200,000 in type A (5%), $100,000 in type B (7%) | |
| D) | $300,000 in type A (5%), $0 in type B (7%) | |
| E) | $110,000 in type A (5%), $190,000 in type B (7%) | |
| Ans: | A | |
| 80. | A company makes two types of telephone answering machines: the standard model and the deluxe model. Each machine passes through three processes: and One standard answering machine requires 2 hours in 5 hours in and 3 hours in One deluxe answering machine requires 3 hours in 5 hours in and 1 hour in Because of employee work schedules, is available for 30 hours, is available for 55 hours, and is available for 27 hours. If the profit is $47 for each standard model and $28 for each deluxe model, how many units of each type should the company produce to maximize profit? | |
| A) | 8 standard models and 3 deluxe models | |
| B) | 9 standard models and 0 deluxe models | |
| C) | 10 standard models and 0 deluxe models | |
| D) | 0 standard models and 10 deluxe models | |
| E) | 3 standard models and 8 deluxe models | |
| Ans: | A | |
| 81. | Find the maximum value of the objective function and where it occurs, if one exists.
Objective function:
Constraints: |
|
| A) | The solution region is empty. There is no maximum value. | |
| B) | The maximum value is 1 and occurs at | |
| C) | The maximum value is 3 and occurs at | |
| D) | The maximum value is 12 and occurs at | |
| E) | The maximum value is 4 and occurs at | |
| Ans: | A | |
| 82. | Find the minimum and maximum values of the objective function and where they occur, subject to the constraints . | |
| A) | The minimum value is 0 at and the maximum value is 32 at . | |
| B) | The minimum value is 0 at and the maximum value is 32 at . | |
| C) | The minimum value is 0 at and the maximum value is 32 at . | |
| D) | The minimum value is 0 at and the maximum value is 32 at . | |
| E) | The minimum value is 0 at and the maximum value is 32 at . | |
| Ans: | A | |
| 83. | Maximize the object function subject to the constraints . | |
| A) | The maximum value is 10 at . | |
| B) | The maximum value is 4 at . | |
| C) | The maximum value is 10 at . | |
| D) | The maximum value is 12 at . | |
| E) | The maximum value is 5 at . | |
| Ans: | D | |
| 84. | Maximize the object function subject to the constraints . | |
| A) | The maximum value is 24 along the line segment connection . | |
| B) | The maximum value is 30 along the line segment connection . | |
| C) | The maximum value is 30 along the line segment connection . | |
| D) | The maximum value is 24 along the line segment connection . | |
| E) | The maximum value is 30 along the line segment connection . | |
| Ans: | C | |
| 85. | Maximize the object function subject to the constraints . | |
| A) | The maximum value is 90 at . | |
| B) | The maximum value is 122 at . | |
| C) | The maximum value is 130 at . | |
| D) | The maximum value is 86 at . | |
| E) | The maximum value is 56 at . | |
| Ans: | D | |
| 86. | Find an objective function that has a minimum value at the indicated vertex D of the constraint region shown below. | |
| A) | Answer will vary. Sample answer: . | |
| B) | Answer will vary. Sample answer: . | |
| C) | Answer will vary. Sample answer: . | |
| D) | Answer will vary. Sample answer: . | |
| E) | Answer will vary. Sample answer: . | |
| Ans: | A | |
| 87. | Find an objective function that has a minimum value at the indicated vertices A and D of the constraint region shown below. | |
| A) | Answer will vary. Sample answer is | |
| B) | Answer will vary. Sample answer is | |
| C) | Answer will vary. Sample answer is . | |
| D) | Answer will vary. Sample answer is | |
| E) | Answer will vary. Sample answer is | |
| Ans: | C | |
| 88. | The costs to a store two models of Global Positioning System (GPS) receivers are $80 and $100. The $80 model yields a profit of $25 and the $100 model yields a profit of $30. Market tests and available resources indicate the following constraints.
The merchant estimates that the total monthly demand will not be exceed 200 units. The merchant does not want to invest more than $18,000 in GPS receiver inventory. What is the optimal inventory level for each model what is optimal profit? |
|
| A) | A maximum profit of $4500 occurs when 180 of each model of GPS receiver is sold. | |
| B) | A maximum profit of $5000 occurs when 200 of each model of GPS receiver is sold. | |
| C) | A maximum profit of $5400 occurs when 180 of each model of GPS receiver is sold. | |
| D) | A maximum profit of $6000 occurs when 200 of each model of GPS receiver is sold. | |
| E) | A maximum profit of $5500 occurs when 100 of each model of GPS receiver is sold. | |
| Ans: | E | |
| 89. | A farming cooperative mixes two brands of cattle feed. Brand X costs $30 per bag, and brand Y costs $25 per bag. Research and available resources have indicated the following constraints.
Brand X contains two units nutritional element A, two units of element B, and two units of element C. Brand Y contains one unit of nutritional element A, nine units of element B, and three units of element C. The minimum requirements for nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively. What is the optimal number of bags of each brand that should be mixed? What is optimal cost? |
|
| A) | To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $540. | |
| B) | To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $320. | |
| C) | To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $240. | |
| D) | To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $300. | |
| E) | To minimize cost, use three bags of brands X and six bags of brand Y for optimal an cost of $360. | |
| Ans: | C | |
| 90. | A humanitarian agency can use two models of vehicles for a refugee rescue mission. Each model A vehicle costs $1000 and each model B vehicle costs $1500. Mission strategies and objectives indicate the following constraints.
A total of at least 20 vehicles must be used. A model A vehicle can hold 45 boxes of supplies.A model B vehicle can hold 30 boxes of supplies. The agency must deliver at least 690 boxes of supplies to the refugee camp. A model A vehicle can hold 20 refugees. A model B vehicle can hold 32 refugees. The agency must rescue at least 520 refugees. What is the optimal number of vehicles of each model that should be used? What is the optimal cost? |
|
| A) | A minimum cost of $27,000 occurs when 6 vehicles of each model are used. | |
| B) | A minimum cost of $27,000 occurs when 14 vehicles of each model are used. | |
| C) | A minimum cost of $34,500 occurs when 23 vehicles of each model are used. | |
| D) | A minimum cost of $26,000 occurs when 26 vehicles of each model are used. | |
| E) | A minimum cost of $25,000 occurs when 10 vehicles of each model are used. | |
| Ans: | E | |
| 91. | A manufacturer produces two models of bicycles. The times (in hours) required for assembling, painting, and packaging each model are shown in the table.
The total times available for assembling, painting, and packing are 4000 hours, 4800 hours, and 1500 hours, respectively. The profit per unit are $50 for model A and $75 for model B. What is the optimal production level for each model? What is the optimal profit? |
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| A) | The optimal profit of $120,000 occurs when no units of model A and 1600 units of of model B are produced. | |||||||||||||
| B) | The optimal profit of $112,000 occurs when no units of model A and 1000 units of of model B are produced. | |||||||||||||
| C) | The optimal profit of $97,500 occurs when no units of model A and 600 units of of model B are produced. | |||||||||||||
| D) | The optimal profit of $60,000 occurs when no units of model A and 0 units of of model B are produced. | |||||||||||||
| E) | The optimal profit of $112,000 occurs when no units of model A and 750 units of of model B are produced. | |||||||||||||
| Ans: | A | |||||||||||||
| 92. | A company makes two models of doghouses. The times (in hours) required for assembling, painting, and packaging are shown in the table.
The total times available for assembling, Painting, and packaging are 4000 hours, 2500 hours, and 1500 hours, respectively. The profits per unit are $60 for model A and $75 for model B. what is the optimal production level for each model? What is the optimal profit? |
|||||||||||||
| A) | The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,571. | |||||||||||||
| B) | The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $98,535. | |||||||||||||
| C) | The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $97,500. | |||||||||||||
| D) | The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $90,000. | |||||||||||||
| E) | The optimal profit occurs when 571 units of model A and 857 units of model B are produced. The optimal profit is $75,000. | |||||||||||||
| Ans: | B | |||||||||||||
| 93. | An accounting firm charges $2500 for an audit and $350 for a tax return. Research and available resources have indicated the following constraints.
The firm has 900 hours of staff time available each week. The firm has 155 hours of review time available each week. Each audit requires 75 hours of staff time and 10 hours of review time. Each tax return requires 12.5 hours of staff time and 2.5 hours of review time. What numbers of audits and tax returns will bring in an optimal revenue? |
|
| A) | The optimal revenue of $0 will occurs when 0 audits and no tax returns are processed. | |
| B) | The optimal revenue of $27,200 will occurs when 5 audits and no tax returns are processed. | |
| C) | The optimal revenue of $21,700 will occurs when 62 audits and no tax returns are processed. | |
| D) | The optimal revenue of $30,000 will occurs when 12 audits and no tax returns are processed. | |
| E) | The optimal revenue of $27,200 will occurs when 42 audits and no tax returns are processed. | |
| Ans: | D | |
| 94. | An accounting firm charges $2500 for an audit and $350 for a tax return. Research and available resources have indicated the following constraints.
The firm has 900 hours of staff time available each week. The firm has 155 hours of review time available each week. Each audit requires 75 hours of staff time and 10 hours of review time. Each tax return requires 12.5 hours of staff time and 2.5 hours of review time. The accounting firm lowers its charge for an audit to $2000. What numbers of audits and tax returns will bring in an optimal revenue? |
|
| A) | The optimal revenue will be $24,700 if the firms does 5 audits and 42 tax returns each week. | |
| B) | The optimal revenue will be $24,000 if the firms does 12 audits and 0 tax returns each week. | |
| C) | The optimal revenue will be $21,700 if the firms does 0 audits and 62 tax returns each week. | |
| D) | The optimal revenue will be $0 if the firms does 0 audits and 0 tax returns each week. | |
| E) | The optimal revenue will be $30,000 if the firms does 12 audits and 0 tax returns each week. | |
| Ans: | A | |
| 95. | A fruit juice company makes two drinks by blending apple and pineapple juices. The percent of apple juice and pineapple juice in each drink are shown in the table.
There are 1000 liters of apple and 1500 liters of pineapple juice available. The profit for drink A is $0.70 per liter and the profit for drink B is $0.60 per liter. What is the optimal production level for each type of drink? What is the optimal profit? |
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| A) | .The optimal profit is $1,666.67 when liters of Drink A and liters Drink B are produced. | ||||||||||
| B) | The optimal profit is $1,666.67 when liters of Drink A and liters Drink B are produced | ||||||||||
| C) | The optimal profit is $1,666.67 when liters of Drink A and liters Drink B are produced. | ||||||||||
| D) | The optimal profit is $1,666.67 when liters of Drink A and liters Drink B are produced. | ||||||||||
| E) | The optimal profit is $1,666.67 when liters of Drink A and liters Drink B are produced. | ||||||||||
| Ans: | B | ||||||||||
| 96. | Maximize the object function subject to the constraints . | |
| A) | The maximum value is 5 at . | |
| B) | The maximum value is 107 at . | |
| C) | The maximum value is 79 at . | |
| D) | The maximum value is 120 at . | |
| E) | The maximum value is 120 at . | |
| Ans: | D | |
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.
