Exam 19: Cost Minimization-Part A

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)=min{su, po F+ 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

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

Suppose that the production function is f (x1, x2)= (min{x1, 2x2}).5.

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 = min{L, 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?

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?

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

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

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

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 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.

A firm has fixed costs of $2,000.Its short-run production function is y = 4x^1/2, 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

The production function for good y is y = max{10x1,4x2}, where x1 and x2 are the amounts of factors 1 and 2.Find the cost function for good y.

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

The production function for drangles is f (x1, x2)= (min{x1, 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

In the short run, a firm which has production function f(L, M)=4L^1/2M^1/2 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

Quasi-fixed costs are those costs that can be avoided if and only if a firm produces zero output.

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 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 firm has production function f (x1, x2, x3, x4)= min{1, x2} +min{x3, 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

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