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

Question

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

answer: $1180

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?

answer: 8

HOW TO SOLVE THESE TWO?

Explanation / Answer

100 = min(x1,20) + min(x3,x4)

Since you want to minimize costs you do not want to use more than 20

Units of x1, then you have:

100 = 20 + min(x3,x4)

then:

min(x3,x4) = 80

Again you want to minimize costs, so you will use the minimum amount

possible of x3 and x4, that is:

x3 = x4 = 80

Now the cost of the production is:

Cost = 20*7 + 20*8 + 80*6 + 80*5 =

     = $1180

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