i just want to know how to find the production level.

Question

A company manufacturers and sells  electric drills per month. The monthly cost and price-demand equations are

C(x) = 61000 + 80x

P(x) = 180 - (x/30)

0<x<5000

(A) Find the production level that results in the maximum revenue.

(B) Find the production level that results in the maximum profit.

(C) Find the price that the company should charge for each drill in order to maximize profit.

I have the answers for B, C as 1500 and 130 respectively.

Answer 1

Revenue = R = P(x)x = 180x - (x)(x/30

For max R take the derivative: 180 - (2/30)x = 0

x = 15(180)= 2700

Profit = P(x) = R(x) - C(x) = 180x -x²/30 - 61000 - 80x = 100x -x²/30 -61000

take the derivative, set = 0, solve for x

-x/15 + 100 = 0

x = 1500

P(x) = P(1500) = 180-x/30 = 180- 1500/30 = 180-50 = 130