Question

​(A) What price should the company charge for the​ phones, and how many phones should be produced to maximize the weekly​ revenue? What is the maximum weekly​ revenue?

Answer 1

Answer:

2500 phones produced at $250 per phone

Max weekly revenue would be $625,000.

Explanation:

p = 500 - 0.1x

p is the price per unit

revenue = quantity * price/unit  

R(x) = revenue = p(x)*x = 500x - 0.1x²

p(x) maximum when first derivative is set to 0

500 - 0.2x = 0 ==> x = 500/0.2 = 2500 quantities

price/unit : p = 500 - 0.1*2500 = 500 - 250 = 250

revenue :  

r(2500) = 500*2500 - 0.1*2500²

r(2500) = 2500(500 - 250) = 625000

The company should produce 2500 phones each week at a price of $250

The maximum weekly revenue is $625000