The total cost of producing x radio sets per day is $( 1/4 x2+ 35x +25), and the price per set at which they may be sold is $(50- 1/2 x)

Question

1. a. What should be the daily output to obtain a maximum total profit?
2. b. Show that the cost of producing a set is a relative minimum at that output.

Answer 1

C= (1/4)x^2 +35x +25 = total cost

P = 50-x/2

Px = R= total revenue = 50x -x^2/2

MR = marginal revenue = 50 -x

MC = marginal cost = x/2 +35

set MC = MR for profit maximizing output level

50-x = x/2+35

3x/2 =15

x =(2/3)15 = 10

Profit = R-C = 50x-x^2/2 - x^2/4 -35x-25

Pr(10) = 50(10) - (10)^2/2 - (10)^2/4 -35(10)-25 =500-50 -25 -350-25 = $50