CHAPTER 21: Cost Minimization
TRUE/FALSE
1. Quasi-fixed costs are those costs that can be avoided if and only if a firm produces zero output.
2. If there are increasing returns to scale, then average costs are a decreasing function of output.
3. If there are increasing returns to scale, then costs per unit of output decrease as you move downward
and to the right along an isocost line.
4. If the production function is f (x1, x2) = minx1, x2, then the cost function is
c(w1, w2, y) = minw1, w2y.
5. The conditional factor demand function for factor 1 is a function x1(w1, w2, y) that tells the ratio of
price to output for an optimal factor choice of the firm.
6. The cost function c(w1, w2, y) expresses the cost per unit of output of producing y units of output if
equal amounts of both factors are used.
7. A competitive, cost-minimizing firm has the production function f (x, y) = x + 2y and uses positive
amounts of both inputs. If the price of x doubles and the price of y triples, then the cost of production
will more than double.
8. The total cost function c(w1, w2, y) expresses the cost per unit of output as a function of input prices
and output.
9. A firm uses a single variable input x to produce outputs according to the production function
f (x) = 300x 6x2. This firm has fixed costs of $400. This firm’s short-run marginal cost curve lies
below its short-run average variable cost curve for all positive values of x.
10. A firm uses a single variable input x to produce outputs according to the production function
f (x) = 300x 6x2. This firm has fixed costs of $300. This firm’s short-run marginal cost curve lies
below its short-run average variable cost curve for all positive values of x.
MULTIPLE CHOICE
1. Lars runs a cookie factory. His cookies are made with sugar, peanut oil, and soybean oil. The number
of boxes of cookies that he produces is f (su, po, so) = minsu, po + 2so, where su is the number of
bags of sugar, po the number of canisters of peanut oil, and so the number of canisters of soybean oil
that he uses. The price of a bag of sugar is $5. The price of a canister of peanut oil is $9. The price of a
canister of soybean oil is $19. If Lars makes 254 boxes of cookies in the
a.
127
b.
0
c.
84.67
d.
169.33
e.
42.33
2. Ben runs a cookie factory. His cookies are made with sugar, peanut oil, and soybean oil. The number
of boxes of cookies that he produces is f (su, po, so) = minsu, po + 2so, where su is the number of
bags of sugar, po the number of canisters of peanut oil, and so the number of canisters of soybean oil
that he uses. The price of a bag of sugar is $12. The price of a canister of peanut oil is $6. The price of
a canister of soybean oil is $19. If Ben makes 254 boxes of cookies in the cheapest way possible, how
many canisters of soybean oil will he use?
a.
169.33
b.
127
c.
0
d.
84.67
e.
42.33
3. A firm’s production function is q = 12x0.50y0.50, where x and y are the amounts of factors x and y that
the firm uses as inputs. If the firm is minimizing unit costs and if the price of factor x is 5 times the
price of factor y,the ratio in which the firm will use factors x and y is closest to
a.
x/y = 0.20.
b.
x/y = 0.40.
c.
x/y = 1.
d.
x/y = 1.67.
e.
x/y = 5.
4. A firm’s production function is q = 26x0.33y0.67, where x and y are the amounts of factors x and y that
the firm uses as inputs. If the firm is minimizing unit costs and if the price of factor x is 6 times the
price of factor y,the ratio in which the firm will use factors x and y is closest to
a.
x/y = 0.08.
b.
x/y = 0.25.
c.
x/y = 0.50.
d.
x/y = 2.40.
e.
x/y = 12.
5. A firm has fixed costs of $4,000. Its short-run production function is y = 4x1/2, where x is the amount of
variable factor it uses. The price of the variable factor is $4,000 per unit. Where y is the amount of
output, the short-run total cost function is
a.
4,000/y + 4,000.
b.
8,000y.
c.
4,000 + 4,000y.
d.
4,000 + 250y2.
e.
4,000 + 0.25y2.
6. A firm has fixed costs of $2,000. Its short-run production function is y = 4x1/2, where x is the amount of
variable factor it uses. The price of the variable factor is $3,000 per unit. Where y is the amount of
output, the short-run total cost function is
a.
5,000y.
b.
2,000 + 3,000y.
c.
2,000/y + 3,000.
d.
2,000 + 187.50y2.
e.
2,000y + 0.19y2.
7. A firm has two factories. One factory has the cost function c1(y1) = 2y21 + 90 and the other has the
cost function c2(y2) = 6y22 + 40. If the firm wishes to produce a total of 32 units as cheaply as
possible, how many units will be produced in the second factory?
a.
7
b.
2
c.
8
d.
14
e.
None of the above.
8. A company can rent one of two copying machines. The first costs $34 a month to rent and costs an
additional 2 cents per copy to use. The second costs $107 a month to rent and an additional 1 cent per
copy to use. How many copies would the company need to make per month in order for it to be
worthwhile to rent the second machine?
a.
7,300
b.
13,300
c.
12,400
d.
6,900
e.
None of the above.
9. A firm produces Ping-Pong balls using two inputs. When input prices are ($15, $7) the firm uses the
input bundle (17, 71). When the input prices are ($12, $24) the firm uses the bundle (77, 4). The
amount of output is the same in both cases. Is this behavior consistent with WACM?
a.
Yes.
b.
No.
c.
It depends on the level of the fixed costs.
d.
We have to know the price of the output before we can test WACM.
e.
It depends on the ratio of variable to fixed costs.
10. As assistant vice president in charge of production for a computer firm, you are asked to calculate the
cost of producing 170 computers. The production function is q = minx, y where x and y are the
amounts of two factors used. The price of x is $18 and the price of y is $10. What is your answer?
a.
$2,580
b.
$4,760
c.
$8,460
d.
$6,180
e.
None of the above.
11. As head of the planning commission of Eastern Motors, your job is to determine where to locate a new
plant. The only inputs used in your cars are steel and labor and the production function is
Cobb-Douglas where f (S, L) = S.5L.5, where S is tons of steel and L is units of labor. You can locate
your plant either in country A or country B. In country A, steel costs $7 a ton and labor costs $7 per
unit. In country B, steel costs $8 per ton and labor costs $6 per unit. In which country should the
company locate its new plant so as to minimize costs per unit of output?
a.
Country A.
b.
Country B.
c.
It doesn’t matter, because the two locations are equally costly.
d.
Country A if output is greater than 14, and country B otherwise.
e.
There is not enough information to enable us to tell.
12. A competitive firm uses two inputs, x and y. Total output is the square root of x times the square root
of y. The price of x is $17 and the price of y is $11. The company minimizes its costs per unit of output
and spends $517 on x. How much does it spend on y?
a.
$766
b.
$480
c.
$655
d.
$517
e.
None of the above.
13. A firm has the production function Q = KL, where K is the amount of capital and L is the amount of
labor it uses as inputs. The cost per unit of capital is a rental fee r and the cost per unit of labor is a
wage w. The conditional labor demand function L(Q, w, r) is
a.
Qwr.
b.
the square root of Qr/w.
c.
Qw/r.
d.
the square root of Qw/r.
e.
Q/wr.
14. Joe’s Bar and Grill uses two inputs, beer and pretzels. When the price of beer was $10 a case and the
price of pretzels was $20 a case, Joe used 1 case of beer and 2 cases of pretzels a day. When the price
of beer was $20 a case and the price of pretzels was $10 a case, Joe used 2 cases of beer and 1 case of
pretzels a day. Joe produced the same output in each of these circumstances.
a.
Joe has a constant returns to scale production function.
b.
Joe has a cost function that exhibits increasing returns.
c.
Joe is not minimizing costs.
d.
Joe’s behavior is consistent with profit maximization.
e.
Joe’s production function exhibits diminishing marginal product.
15. The production function for drangles is f (x1, x2) = (minx1, 3x2)1/2, where x1 is the amount of sugar
and x2 is the amount of dough used. At the factor prices, w1= w2 = $1, the minimum cost of producing
y drangles is
a.
4y1/2.
b.
(3/4)y1/2.
c.
(3/4)y2.
d.
(4/3)y2.
e.
None of the above.
16. An orange grower has discovered a process for producing oranges that requires two inputs. The
production function is Q = min2x1, x2, where x1 andx2 are the amounts of inputs 1 and 2 that he
uses. The prices of these two inputs are w1 = $5 and w2 = $2,respectively. The minimum cost of
producing 140 units is therefore
a.
$980.
b.
$630.
c.
$1,400.
d.
$280.
e.
$700.
17. An orange grower has discovered a process for producing oranges that requires two inputs. The
production function is Q = min2x1, x2, where x1 and x2 are the amounts of inputs 1 and 2 that he
uses. The prices of these two inputs are w1 = $5 and w2 = $10, respectively. The minimum cost of
producing 160 units is therefore
a.
$2,000.
b.
$2,400.
c.
$800.
d.
$8,000.
e.
$1,600.
18. Roberta runs a dress factory. She produces 50 dresses per day, using labor and electricity. She uses a
combination of labor and electricity that produces 50 dresses per day in the cheapest possible way. She
can hire as much labor as she wants at a cost of 20 cents per minute. She can use as much electricity as
she wants at a cost of 10 cents per minute. Her production isoquants are smooth curves without kinks
and she uses positive amounts of both inputs.
a.
The marginal product of a kilowatt-hour of electricity is twice the marginal product of a
minute of labor.
b.
The marginal product of a minute of labor is twice the marginal product of a kilowatt-hour
of electricity.
c.
The marginal product of a minute of labor is equal to the marginal product of a
kilowatt-hour of electricity.
d.
There is not enough information to determine the ratio of marginal products. We’d have to
know the production function to know this.
e.
The marginal product of a minute of labor plus the marginal product of a kilowatt-hour of
labor must equal 50/(20 + 10).
19. A competitive firm has the three-factor production function f (x, y, z) = (x + y)1/2 z 1/2. The factor prices
used to be wx = $1, wy = $2, and wz = $3. Suppose that the price of factor y doubled while the other
two prices stayed the same. Then the cost of production
a.
increased by more than 10% but less than 50%.
b.
increased by 50%.
c.
doubled.
d.
stayed the same.
e.
increased by more than 50% but did not double.
20. A competitive firm uses three factors of production. Its production function is f (x, y, z) = (x + y)1/2 z 1/2.
Originally the factor prices were wx = $1, wy = $2, and wz = $3. The prices of factors x and z
decreased to half of their previous levels, but the price of factor y stayed constant. The cost of
production
a.
decreased by more than 1/2.
b.
decreased by 1/3.
c.
decreased by exactly 1/2.
d.
stayed constant.
e.
decreased by less than 1/3.
21. A competitive firm with output y has a production function y = (2x1 + x2)1/2, where x1 and x2 are inputs
used in production. The firm produces the output minimizing cost. With input prices w1 and w2, which
of the following is true?
a.
The firm has L-shaped isoquants.
b.
The firm must use the cheaper input.
c.
The firm must use only input x1 if w1 2w2.
d.
The technology has increasing returns to scale.
e.
More than one of the above is true.
22. Suppose that the production function is f (x1, x2) = (minx1, 2x2).5.
a.
There are constant returns to scale.
b.
The cost function is a min function.
c.
If the price of x1 is more than twice the price of x2, only x2 is used in production.
d.
A cost-minimizing firm producing 5 units of output will use 25 units of x1 and some x2.
e.
The cost function is a linear function of output.
23. If the production function is given by f (x1,x2, x3, x4) = minx1, x2 + minx3, x4 and the prices of
inputs (x1,x2, x3, x4) are (2, 1, 5, 3), the minimum cost of producing 1 unit of output is closest to
a.
$1.
b.
$3.
c.
$4.
d.
$8.
e.
$11.
24. Two firms, Wickedly Efficient Widgets (WEW) and Wildly Nepotistic Widgets (WNW), both produce
widgets, using the same production function y = K1/2L1/2, where K is the amount of labor used and L is
the amount of capital used. Each company can hire labor at $1 per unit of labor and capital at $1 per
unit. Each company produces 10 widgets per week. WEW chooses its input combinations to produce
in the cheapest way possible. Although it produces the same output per week as WEW, WNW is
required by its dotty CEO to use twice as much labor as WEW. How much higher are WNW’s total
costs per week than WEW’s?
a.
$5
b.
$10
c.
$15
d.
$2.50
e.
$2
25. Two firms, Wickedly Efficient Widgets (WEW) and Wildly Nepotistic Widgets (WNW), both produce
widgets, using the same production function y = K1/2L1/2, where K is the amount of labor used and L is
the amount of capital used. Each company can hire labor at $1 per unit of labor and capital at $9 per
unit. Each company produces 90 widgets per week. WEW chooses its input combinations to produce
in the cheapest way possible. Although it produces the same output per week as WEW, WNW is
required by its dotty CEO to use twice as much labor as WEW. How much higher are WNW’s total
costs per week than WEW’s?
a.
$270
b.
$67.50
c.
$275
d.
$135
e.
$132
26. A new metal alloy is discovered that uses copper and zinc in fixed proportions where each unit of the
alloy requires 4 units of zinc and 2 units of copper. If no other inputs are required, if the price of zinc
is $2 per unit, and the price of copper is $5 per unit and if total output is 4,000 units, what is the
average cost per unit of output?
a.
$.50
b.
$2
c.
$18
d.
$20
e.
$25
27. A new metal alloy is discovered that uses copper and zinc in fixed proportions where each unit of the
alloy requires 2 units of zinc and 2 units of copper. If no other inputs are required, if the price of zinc
is $3 per unit, and the price of copper is $3 per unit and if total output is 5,000 units, what is the
average cost per unit of output?
a.
$6
b.
$1.50
c.
$12
d.
$15
e.
$18
28. The production function is f (L, M) = 4L1/2M1/2, where L is the number of units of labor and M is the
number of machines. If the amounts of both factors can be varied and if the cost of labor is $64 per
unit and the cost of using machines is $1 per machine, then the total cost of producing 20 units of
output is
a.
$80.
b.
$650.
c.
$20.
d.
$320.
e.
$40.
29. The production function is f (L, M) = 5L1/2M1/2, where L is the number of units of labor and M is the
number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit
and the cost of using machines is $64 per machine, then the total cost of producing 12 units of output
is
a.
$438.
b.
$108.
c.
$576.
d.
$115.20.
e.
$57.60.
30. Douffelberry juice is a mild intoxicant, prized for facilitating conversation among university
administrators but not otherwise valued. The berry does not travel well,so it must be squeezed on the
farm where it is grown.Baskets of berries, B, are produced using ounces of seeds, S, and hours of
labor, L, according to a production function B = S1/2L1/2. Gallons of juice, J, are made from baskets of
berries and hours of labor according to the production function J = minB, L. If seeds cost $16 per
ounce and labor costs $1 per hour, what is the cost of producing each gallon of douffelberry juice?
a.
$18
b.
$8
c.
$4
d.
$9
e.
Since there are not constant returns to scale, the cost per gallon depends on the number of
gallons produced.
31. Douffelberry juice is a mild intoxicant, prized for facilitating conversation among university
administrators but not otherwise valued. The berry does not travel well,so it must be squeezed on the
farm where it is grown.Baskets of berries, B, are produced using ounces of seeds, S, and hours of
labor, L, according to a production function B = S1/2L1/2. Gallons of juice, J, are made from baskets of
berries and hours of labor according to the production function J = minB, L. If seeds cost $9 per
ounce and labor costs $9 per hour, what is the cost of producing each gallon of douffelberry juice?
a.
$27
b.
$54
c.
$9
d.
$18
e.
Since there are not constant returns to scale, the cost per gallon depends on the number of
gallons produced.
32. Nadine has a production function 2x1 + x2. If the factor prices are $8 for factor 1 and $5 for factor 2,
how much will it cost her to produce 70 units of output?
a.
$1,470
b.
$280
c.
$350
d.
$910
e.
$315
33. Nadine has a production function 4x1 + x2. If the factor prices are $12 for factor 1 and $2 for factor 2,
how much will it cost her to produce 30 units of output?
a.
$795
b.
$60
c.
$90
d.
$1,500
e.
$75
34. The production function is f (L, M) = 4L1/2M1/2, where L is the number of units of labor and M is the
number of machines used. If the cost of labor is $49 per unit and the cost of machines is $16 per unit,
then the total cost of producing 5 units of output will be
a.
$70.
b.
$162.50.
c.
$80.
d.
$140.
e.
None of the above.
35. The production function is f (L, M) = 4L1/2M1/2, where L is the number of units of labor and M is the
number of machines used. If the cost of labor is $36 per unit and the cost of machines is $4 per unit,
then the total cost of producing 6 units of output will be
a.
$72.
b.
$36.
c.
$120.
d.
$24.
e.
None of the above.
36. In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the
cost of labor is $4 per unit and the cost of machines is $10 per unit, the short-run total cost of
producing 72 units of output is
a.
$504.
b.
$288.
c.
$720.
d.
$728.
e.
$364.
37. In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the
cost of labor is $4 per unit and the cost of machines is $4 per unit, the short-run total cost of producing
48 units of output is
a.
$192.
b.
$196.
c.
$198.
d.
$320.
e.
$160.
38. Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of plastic and x2 is
the amount of wood used. If the cost of plastic is $6 per unit and the cost of wood is $1 per unit, then
the cost of producing 5 deer is
a.
$25.
b.
$65.
c.
$75.
d.
$5.
e.
$15.
39. Al’s production function for deer is f(x1, x2) = (2x1 + x2)1/2, where x1 is the amount of plastic and x2 is
the amount of wood used. If the cost of plastic is $6 per unit and the cost of wood is $1 per unit, then
the cost of producing 7 deer is
a.
$147.
b.
$49.
c.
$7.
d.
$91.
e.
$21.
40. A firm has production function f (x1, x2, x3, x4) = minx1, x2 + minx3, x4. This firm faces
competitive factor markets where the prices for the four factors are w1 = $7, w2 = $8, w3 = $6, and w4
= $5. The firm must use at least 20 units of factor 2. The cost of producing 100 units in the cheapest
possible way is
a.
$1,400.
b.
$1,200.
c.
$1,340.
d.
$1,180.
e.
$500.
41. A firm has production function f (x1, x2, x3, x4) = minx1, x2 + minx3, x4. This firm faces
competitive factor markets where the prices for the four factors are w1 = $4, w2 = $8, w3 = $5, and w4
= $3. The firm must use at least 20 units of factor 2. The cost of producing 100 units in the cheapest
possible way is
a.
$700.
b.
$1,040.
c.
$880.
d.
$1,300.
e.
$300.
42. The law firm of Dewey, Cheatham, and Howe specializes in accident injury claims. The firm charges
its clients 25% of any damage award given. The only cost to the firm of producing an accident injury
claim is the time spent by a junior partner working on the case. Junior partners are paid $100 per hour
for this drudgery. If the firm is suing for damages of $640,000 and if its chances of winning a case are
1/25h, where h is the number of hours spent working on the case, then to maximize its profits, how
many hours should it have the junior partner spend working on the case?
a.
24
b.
40
c.
8
d.
12
e.
None of the above.
43. The law firm of Dewey, Cheatham, and Howe specializes in accident injury claims. The firm charges
its clients 25% of any damage award given. The only cost to the firm of producing an accident injury
claim is the time spent by a junior partner working on the case. Junior partners are paid $100 per hour
for this drudgery. If the firm is suing for damages of $250,000 and if its chances of winning a case are
1/25h, where h is the number of hours spent working on the case, then to maximize its profits, how
many hours should it have the junior partner spend working on the case?
a.
7.50
b.
5
c.
25
d.
15
e.
None of the above.
44. A firm with the production function f (x1, x2, x3, x4) = minx1, x2, x3, x4 faces input prices
w1 = $1, w2 = $5,w3 = $5, w4 = $3 for factors 1, 2, 3, and 4. The firm must use at least 10 units of
factor 2. The lowest cost at which it can produce 100 units of output is
a.
$800.
b.
$440.
c.
$1,400.
d.
$770.
e.
$400.
45. A firm with the production function f (x1, x2, x3, x4) = minx1, x2, x3, x4 faces input prices
w1 = $1, w2 = $2,w3 = $2, w4 = $5 for factors 1, 2, 3, and 4. The firm must use at least 17 units of
factor 2. The lowest cost at which it can produce 100 units of output is
a.
$1,000.
b.
$400.
c.
$317.
d.
$615.
e.
$300.
46. If output is produced according to Q = 4L + 6K, the price of K is $24, and the price of L is $20, then
the cost-minimizing combination of K and L capable of producing 72 units of output is
a.
L = 9 and K = 6.
b.
L = 20 and K = 24.
c.
L = 18 and K = 12.
d.
L = 0 and K = 12.
e.
L = 18 and K = 0.
47. If output is produced according to Q = 4L + 6K, the price of K is $12, and the price of L is $20, then
the cost-minimizing combination of K and L capable of producing 96 units of output is
a.
L = 20 and K = 12.
b.
L = 0 and K = 16.
c.
L = 24 and K = 16.
d.
L = 12 and K = 8.
e.
L = 24 and K = 0.
48. If output is produced according to Q = 4LK, the price of K is $10, and the price of L is $40, then the
cost minimizing cost minimizing combination of K and L capable of producing 64 units of output is
a.
L = 16 and K = 1.
b.
L = 2 and K = 8.
c.
L = 2 and K = 2.
d.
L = 32 and K = 32.
e.
L = 1 and K = 16.
49. If output is produced according to Q = 4LK, the price of K is $10, and the price of L is $5, then the cost
minimizing combination of K and L capable of producing 2 units of output is
a.
L = 0.35 and K = 0.35.
b.
L = 1 and K = 0.50.
c.
L = 0.50 and K = 1.
d.
L = 1 and K = 1.
e.
L = 1 and K = 0.50.
50. If it costs $20 to set up and later clean a bagel press and bagels cost $1 per week per bagel to store,
how many times should the bagel press be run each week to produce 1,000 bagels a week to be sold
continuously?
a.
Once
b.
Twice
c.
3 times
d.
4 times
e.
5 times
51. If it costs $20 to set up and later clean a bagel press and bagels cost $1 per week per bagel to store,
how many times should the bagel press be run each week to produce 360 bagels a week to be sold
continuously?
a.
Twice
b.
4 times
c.
Once
d.
3 times
e.
5 times
52. A politician facing reelection can win votes according to the following process: V = 500S0.20M0.60,
where S is hours of making campaign speeches and M is the number of flyers mailed. Making
speeches costs $10 per hour, mailing flyers costs $.50 per flyer, and $8,000 are available to spend on
the campaign. Assuming the politician wants to maximize votes, how should the budget be allocated
between speeches and mailing flyers?
a.
No speeches should be given; 16,000 flyers should be mailed.
b.
400 hours of speeches should be given; 8,000 flyers should be mailed out.
c.
200 hours of speeches should be given; 12,000 flyers should be mailed out.
d.
2,000 hours of speeches should be given; 6,000 flyers should be mailed out.
e.
800 hours speeches should be given; no flyers should be mailed out.
53. A politician facing reelection can win votes according to the following process: V = 500S0.20M0.60,
where S is hours of making campaign speeches and M is the number of flyers mailed. Making
speeches costs $10 per hour, mailing flyers costs $.50 per flyer, and $2,000 are available to spend on
the campaign. Assuming the politician wants to maximize votes, how should the budget be allocated
between speeches and mailing flyers?
a.
No speeches should be given; 4,000 flyers should be mailed.
b.
100 hours of speeches should be given; 2,000 flyers should be mailed out.
c.
50 hours of speeches should be given; 3,000 flyers should be mailed out.
d.
500 hours of speeches should be given; 1,500 flyers should be mailed out.
e.
200 hours speeches should be given; no flyers should be mailed out.
54. The Chrysler Belvedere Truck Plant is attempting to minimize production costs. Over one month,
3,200 fenders are needed on the production line, which runs continuously. If it costs $400 to set up the
stamping press to produce fenders and $1 per month to store produced fenders, how many times
should the stamping press be run per month?
a.
Once
b.
Twice
c.
3 times
d.
4 times
e.
5 times
55. The Chrysler Belvedere Truck Plant is attempting to minimize production costs. Over one month,
1,600 fenders are needed on the production line, which runs continuously. If it costs $200 to set up the
stamping press to produce fenders and $1 per month to store produced fenders, how many times
should the stamping press be run per month?
a.
4 times
b.
Twice
c.
Once
d.
3 times
e.
5 times
56. A lobbyist in our nation’s capitol must buy 250 votes in the House of Representatives and Senate to
win passage of a bill to add Millard Fillmore’s face to Mount Rushmore. Votes in Congress can be
purchased according to the following process: V = CM/100,000, where C is the number of dollars
contributed to campaign funds and M is the number of three-martini lunches. If three-martini lunches
cost $64 each, what is the smallest expenditure the lobbyist could make to ensure Mr. Fillmore’s
proper place in history?
a.
$80,000
b.
$390,625
c.
$25,000,064
d.
$325,000
e.
$25,000,000
57. A lobbyist in our nation’s capitol must buy 250 votes in the House of Representatives and Senate to
win passage of a bill to add Millard Fillmore’s face to Mount Rushmore. Votes in Congress can be
purchased according to the following process: V = CM/100,000, where C is the number of dollars
contributed to campaign funds and M is the number of three-martini lunches. If three-martini lunches
cost $25 each, what is the smallest expenditure the lobbyist could make to ensure Mr. Fillmore’s
proper place in history?
a.
$1,000,000
b.
$25,000,025
c.
$130,000
d.
$50,000
e.
$25,000,000
58. The editors at Snoozeweek, a news magazine, constantly alter the proportion of celebrity photographs
and mundane news stories so as to maximize the number of copies sold. A statistical consultant has
estimated sales to be S = 1,000C 0.60N 0.60, where C is the number of celebrity photographs and N is
column inches of news stories. If the editors only have $8,000 to spend on each edition with celebrity
photos costing $200 each and news stories costing $10 per column inch, what should the editors do
a.
Purchase 23 celebrity photos and 340 column inches of news stories.
b.
Purchase 20 celebrity photos and 400 column inches of news stories.
c.
Purchase 25 celebrity photos and 300 column inches of news stories.
d.
Purchase 16 celebrity photos and 480 column inches of news stories.
e.
Purchase 15 celebrity photos and 500 column inches of news stories.
59. The editors at Snoozeweek, a news magazine, constantly alter the proportion of celebrity photographs
and mundane news stories so as to maximize the number of copies sold. A statistical consultant has
estimated sales to be S = 1,000C0.60N 0.50, where C is the number of celebrity photographs and N is
column inches of news stories. If the editors only have $11,000 to spend on each edition with celebrity
photos costing $400 each and news stories costing $10 per column inch, what should the editors do?
a.
Purchase 10 celebrity photos and 700 column inches of news stories.
b.
Purchase 15 celebrity photos and 500 column inches of news stories.
c.
Purchase 11 celebrity photos and 660 column inches of news stories.
d.
Purchase 13 celebrity photos and 580 column inches of news stories.
e.
Purchase 20 celebrity photos and 300 column inches of news stories.
60. Vincent Smudge, an avant-garde New York artist,creates “living sculpture” by smearing paint slowly
all over himself. S hours of “living sculpture” can be created by S = minL, T/3, where L is hours of
labor by Mr. Smudge and T is tubes of water-soluble paint.Since Mr. Smudge is a highly renowned
artist, his labor costs $50 per hour, while paint costs $10 per tube.Using a $3,000 grant from the
National endowment for the Arts, how many hours of “living sculpture” can Mr. Smudge create?
a.
50
b.
56.25
c.
37.50
d.
750
e.
2,250
61. Vincent Smudge, an avant-garde New York artist,creates “living sculpture” by smearing paint slowly
all over himself. S hours of “living sculpture” can be created by S = minL, T/5, where L is hours of
labor by Mr. Smudge and T is tubes of water-soluble paint.Since Mr. Smudge is a highly renowned
artist, his labor costs $200 per hour, while paint costs $40 per tube.Using a $10,000 grant from the
National Endowment for the Arts, how many hours of “living sculpture” can Mr. Smudge create?
a.
1,666.67
b.
48.08
c.
41.67
d.
25
e.
8,333.33
62. Using existing plant and equipment, Priceless Moments Figurines can be manufactured using plastic,
clay, or any combination of these materials. A figurine can be manufactured by F = 4P + 2C, where P
is pounds of plastic and C is pounds of clay. Plastic costs $2 per pound and clay costs $5 per pound.
What would be the lowest cost of producing 40,000 figurines?
a.
$20,000
b.
$100,000
c.
$60,000
d.
$10,000
e.
$40,000
63. Using existing plant and equipment, Priceless Moments Figurines can be manufactured using plastic,
clay, or any combination of these materials. A figurine can be manufactured by F = 2P + 5C, where P
is pounds of plastic and C is pounds of clay. Plastic costs $5 per pound and clay costs $2 per pound.
What would be the lowest cost of producing 60,000 figurines?
a.
$30,000
b.
$24,000
c.
$87,000
d.
$150,000
e.
$60,000
64. Rocco’s Pasta Bar makes manicotti according to an old family recipe which states M = min3/2C, 3P,
where M, C, and P are pounds of manicotti, cheese, and pasta respectively. If cheese costs $3 per
pound and pasta costs $1 per pound, how much would it cost to produce 10 pounds of manicotti in the
cheapest way possible?
a.
$3.33
b.
$20
c.
$23.33
d.
$35
e.
$10
65. Rocco’s Pasta Bar makes manicotti according to an old family recipe which states M = min5/4C, 5P,
where M, C, and P are pounds of manicotti, cheese, and pasta respectively. If cheese costs $3 per
pound and pasta costs $4 per pound, how much would it cost to produce 20 pounds of manicotti in the
cheapest way possible?
a.
$64
b.
$48
c.
$16
d.
$33.33
e.
$20
PROBLEM
1. A firm has a production function described as follows:“Weekly output is equal to the square root of the
minimum of the amount of capital and the number of hours of labor used per week.” Suppose that the
cost of a unit of capital is r and the price of a unit of labor is w and the level of output is y. Write down
the long-run total cost as a function of w, r, and y.
2. The production function for good y is y = max10x1,4x2, where x1 and x2 are the amounts of factors
1 and 2. Find the cost function for good y.
3. If the production function for tuna casseroles is minx1,x2 2, where x1 is the amount of factor 1 and
x2 is the amount of factor x2, find the cost function for tuna casseroles.
4. 4. The cost function c(w1, w2, y) of a firm gives the cost of producing y units of output when the wage
of factor 1 is w1 and the wage of factor 2 is w2. Find the cost functions for the following firms:
a. A firm with production function f (x1, x2) = min2x1, 3x2
b. A firm with production function f (x1, x2) = 2x1 + 3x2
c. A firm with production function f (x1, x2) = max2x1, 3x2
