Question

3) A company manufactures and sells x cellphones per week. The weekly cost and price-demand equations are

Cx=5,000+84x

p(x)=300-0.2x

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

b) What is the maximum weekly profit? How much should the company charge for the phones, and how many phones should be produced to realize the maximum weekly profit?

Answer 1

Solution -

Given - Cost and price demand equations are

  

  

a) Revenue function

  

For maximum revenue, we differentiate revenue function

  

  

The second derivative is negative so revenue will be maximum at x =750

So 750 phones should be produced to maximize weekly revenue.

So price should $150 to maximize weekly revenue.     

Maximum revenue

b) Profit

Differentiating it with respect to x both sides

  

  

  

   The second derivative is negative so profit will be maximum at x = 540

So 540 phones should be produced to maximize weekly profit.

   So price should $192 to maximize weekly revenue.  

Maximum profit

  

   $