Exam 19: Cost Minimization

The production function is f (L, M) = 4 , 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

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?

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?

An orange grower has discovered a process for producing oranges that requires two inputs. The production function is Q = min{2x1, 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

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 firm with the production function f (x1, x2, x3, x4) =min{x1, 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

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= min{x, 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 competitive firm uses three factors of production. Its production function is f (x, y, z) = . 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

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{ , 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 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?

In the short run, a firm which has production function f (L, M) = 4 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

If the production function is f (x1, x2) = min{x1, x2},then the cost function is c(w1, w2, y) = min{w1, w2}y.

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 = . Gallons of juice, J, are made from baskets of berries and hours of labor according to the production function J = min{B, 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 firm has production function f (x1, x2, x3, x4) =min{x1, x2} + min{x3, x4}. This firm faces competitive factor markets where the prices for the four factors arew1 = $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

The total cost function c(w1, w2, y) expresses the cost per unit of output as a function of input prices and output.

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 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?

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) = min{su, 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?

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?

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 = . Gallons of juice, J, are made from baskets of berries and hours of labor according to the production function J = min{B, L}. If seeds cost $16 per ounce and labor costs $1 per hour, what is the cost of producing each gallon of douffelberry juice?