Max rev and profit?

Question

A company manufactures and sells x digital cameras per week. The weekly price demand and cost are p=400-0.4x and c(x)=2000+160x

1. what price should the company charge for cameras, and how many cameras should be produced to maximize the weekly revenue? What is the maximum revenue?

2. What is the maximum profit? How much should the company charge for the cameras, and how many cameras should be produced to realize the maximum profit?

Thank you

Answer 1

1:

TR=P*X=(400-0.4X)*X

Revenue maximization: MR=0

MR=(TR)'=400-0.8X

400-0.8X=0

0.8X=400

X=500

P=400-0.4*500=300

TR=500*300=150'000

2:

TR=P*X=(400-0.4X)*X

TC=2000+160X

Profit maximization MC=MR

MC=(TC)'=160

MR=(TR)'=400-0.8X

160=400-0.8X

0.8X=240

X=300

P=400-0.4*300=400-120=280

TR=280*300=84'000

Profit=TR-TC

TC=2000+160*300=50'000

Profit=84'000-50'000=34'000