Exam 19: Cost Minimization-Part A

The production function is f (L, M)=4L^1/2M^1/2, 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

If the production function is given by f (x1,x2, x3, x4)= min{x1, x2} + min{x3, 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

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 $4 per unit, the short-run total cost of producing 48 units of output is

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/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?

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 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?

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

The production function is f (L, M)=4L^1/2M^1/2, 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

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?

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.

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

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 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

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.

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

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 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?

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 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.

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M = min{3/2C, 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?

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?