Question

1) Suppose a firm faces the following demand curve: q(p) = 100,000– 7,250p and it costs them $5 to make each unit of their product and their fixed costs are $15,000.

(show your work)

a. What price will the firm charge? Round your answer to the nearest 2 decimal places.

b. At that price found in #25 what quantity will they produce? Round your answer to

       the nearest whole unit.

c. What are the break-even prices? Round your answers to the nearest two decimal

       places.

d. What is the highest profit they can make? Round your answer to the nearest dollar.

Answer 1

Total cost of production =5q+15000 = 5*(100000-7250p)+15000

a) Profit, W = Total revenue - total cost

W = pq- (5*(100000-7250p)+15000) = p*(100,000– 7,250p) - (5*(100000-7250p)+15000)

To maximize W

dW/dp = 0

dW/dp = 100,000– 14500p + 36250 = 0

14500p =63750

p= 9.40

Price = $9.4

b) Quantity = 100000-7250*9.4 = 31850

c) Let breakeven price = p

Total revenue = total cost

p*(100,000– 7,250p) = 5*(100000-7250p)+15000

7250p^2 -136250p +515000 = 0

p =5.24 and 13.55

Break even prices are 5.24 and 13.55.

d) highest profit = profit at price 9.4

Profit = 9.4*31850-31850*5-15000 =$125140