Exam 21:Cost Minimization-Part A

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?

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?

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?

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.

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 =S^1/2L^1/2.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?

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 +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=1,000C0.60N 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?

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

The production function is f (L,M)=5L^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 $9 per unit and the cost of using machines is $64 per machine,then the total cost of producing 12 units of output is

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 andx2 are the amounts of inputs 1 and 2 that he uses.The prices of these two inputs are w1 =0 $5 and w2 =$2,respectively.The minimum cost of producing 140 units is therefore

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 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?

Rocco's Pasta Bar makes manicotti according to an old family recipe which states M=min{5/4C,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?

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.

A politician facing reelection can win votes according to the following process: V=500S^0.20M^0.60,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 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?

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?

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 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