# Suppose you buy a piece of office equipment for \$19,000. After 7 years

August 30, 2017

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Quiz 1

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Question 1

Suppose you buy a piece of office equipment for \$19,000. After 7 years you sell it for a scrap value of \$4,000. The equipment is depreciated linearly over 7 years. The rate of depreciation of the piece of equipment is

a)
\$2,500.00 per year

b)
\$2,714.29 per year

c)
\$15,000.00 per year

d)
\$1,875.00 per year

e)
\$2,142.86 per year

f)
None of the above.

Question 2

A truck is worth \$70,000.00 when purchased. It is depreciated linearly over 5 years and has a scrap value of \$10,000.00. A linear equation expressing the truck’s book value at the end of t years is

a)
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b)
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c)
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d)
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e)
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f)
None of the above.

Question 3

Suppose you buy a piece of office equipment for \$9,000.00. After 6 years you sell it for a scrap value of \$5,000.00. The equipment is depreciated linearly over 6 years. The value of the piece of equipment after 4 years is (rounded to the nearest whole dollar)

a)
\$6,714.00

b)
\$7,222.00

c)
\$8,467.00

d)
\$5,000.00

e)
\$6,333.00

f)
None of the above.

Question 4

You did not answer the question.

A company has fixed monthly costs of \$100,000 and production costs on its product of \$19 per unit. The company sells its product for \$64 per unit. The cost function, revenue function and profit function for this situation are

a)
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b)
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c)
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d)
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e)
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f)
None of the above.

Question 5

A manufacturer has a monthly fixed cost of \$30,000 and a production cost of \$11 for each unit produced. The product sells for \$24 per unit. If the manufacturer produces and sells 13,000 units one month, then his profit is

a)
\$1,430,000

b)
\$113,000

c)
\$139,000

d)
\$3,120,000

e)
\$282,000

f)
None of the above.

Question 6

A manufacturer has a monthly fixed cost of \$40,000 and a production cost of \$8 for each unit produced. The product sells for \$15 per unit. If the manufacturer produces and sells 3,000 units per month, indicate whether he will have a profit, loss or break-even.

a)
Break-even

b)
Profit

c)
Loss

d)
None of the above.

Question 7

A manufacturer has a monthly fixed cost of \$180,000 and a production cost of \$54 for each unit produced. The product sells for \$90 per unit. Find the break-even quantity.

a)
2,500

b)
1,250

c)
2,000

d)
450,000

e)
5,000

f)
None of the above.

Question 8

A manufacturer has a monthly fixed cost of \$70,000 and a production cost of \$18 for each unit produced. The product sells for \$35 per unit. Find the break-even revenue.

a)
\$144,117.65

b)
\$2,500.00

c)
\$4,117.65

d)
\$1,320.75

e)
\$2,000.00

f)
None of the above.

Question 9

A manufacturer has a monthly fixed cost of \$100,000 and a production cost of \$20 for each unit produced. The product sells for \$31 per unit. Find the break-even point.

a)
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b)
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c)
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d)
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e)
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f)
None of the above.

Question 10

Use the feasible set shown to find the optimal value to maximize the objective function P = 46x + 33y.

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a)
263

b)
259

c)
264

d)
262

e)
267

f)
None of the above.

Question 11

Given the linear programming problem, use the method of corners to determine where the minimum occurs and give the minimum value.

Minimize

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Subject to
x ≤ 8
y ≤ 10
x + y ≥ 10
x ≥ 0
y ≥ 0

a)
( 8 , 0 ) with C = 8

b)
( 8 , 10 ) with C = 28

c)
( 0 , 0 ) with C = 0

d)
( 8 , 2 ) with C = 12

e)
( 0 , 10 ) with C = 20

f)
None of the above.

Question 12

You did not answer the question.

A company produces two types of nutritional supplements; Energize and Excel. Energize contains 28 mg of vitamin A, 78 mg of vitamin C and 15 mg of an herbal supplement. Excel contains 51 mg of vitamin A, 62 mg of vitamin C and 17 mg of the herbal supplement. An athlete is told that he needs at least 542 mg of vitamin A, 1191 mg of vitamin C and 308 mg of the herbal supplement for optimal athletic performance. The athlete wants to take the supplements, but at the lowest possible cost. Energize pills cost 50 cents each, while Excel pills cost 110 cents each. Let x = the number of Energize pills to take, and let y = the number of Excel pills to take. Which of the following is the objective function for this situation?

a)
Minimize C = 50x + 110y

b)
Maximize C = 110x + 50y

c)
Maximize C = 50x + 110y

d)
Minimize C = 110x + 50y

e)
Minimize C = 11910x + 3080y

f)
None of the above.

Question 13

A company produces two types of nutritional supplements; Energize and Excel. Energize contains 24 mg of vitamin A, 65 mg of vitamin C and 45 mg of an herbal supplement. Excel contains 57 mg of vitamin A, 68 mg of vitamin C and 21 mg of the herbal supplement. An athlete is told that he needs at least 449 mg of vitamin A, 1378 mg of vitamin C and 474 mg of the herbal supplement for optimal athletic performance. The athlete wants to take the supplements, but at the lowest possible cost. Energize pills cost 50 cents each, while Excel pills cost 130 cents each. Let x = the number of Energize pills to take, and let y = the number of Excel pills to take. What are the constraints for this problem?

a)
24x + 57y ≤ 449, 57x + 68y ≤ 1378, 45x + 21y ≤ 474, x ≥ 0, y ≥ 0

b)
24x + 57y ≥ 449, 65x + 68y ≥ 1378, 45x + 21y ≥ 474, x ≥ 0, y ≥ 0

c)
24x + 65y ≥ 449, 57x + 68y ≥ 1378, 45x + 21y ≥ 474, x ≥ 0, y ≥ 0

d)
24x + 57y ≤ 449, 65x + 68y ≥ 1378, 45x + 21y ≤ 474, x ≥ 0, y ≥ 0

e)
24x + 57y ≥ 449, 65x + 68y ≤ 1378, 45x + 21y ≥ 474, x ≥ 0, y ≥ 0

f)
None of the above.

Question 14

A certain academic department at a local university will conduct a research project. The department will need to hire graduate research assistants and professional researchers. Each graduate research assistant will need to work 27 hours per week on fieldwork and 13 hours per week at the university’s research center. Each professional researcher will need to work 14 hours per week on fieldwork and 26 hours per week at the university’s research center. The minimum number of hours needed per week for fieldwork is 151 and the minimum number of hours needed per week at the research center is 131. Each research assistant will be paid \$251 per week and each professional researcher will be paid \$455 per week. Let x denote the number of graduate research assistants hired and let y denote the number of professional researcher hired. The department wants to minimize cost. Set up the Linear Programming Problem for this situation.

a)
Min C = 251x + 455y; s.t 14x + 27y ≤ 131, 26x + 13y ≤ 151, x ≥ 0, y ≥ 0

b)
Min C = 455x + 251y; s.t 27x + 13y ≥ 151, 14x + 26y ≥ 131, x ≥ 0, y ≥ 0

c)
Min C = 251x + 455y; s.t 27x + 14y ≥ 151, 26x + 13y ≥ 131, x ≥ 0, y ≥ 0

d)
Min C = 251x + 455y; s.t 27x + 14y ≥ 151, 13x + 26y ≥ 131, x ≥ 0, y ≥ 0

e)
Min C = 455x + 251y; s.t 14x + 27y ≥ 151, 26x + 13y ≥ 131, x ≥ 0, y ≥ 0

f)
None of the above.

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