Question

How would you solve this problem??

Answer 1

x = 14000

Explanation:

Function representing the cost to the company,

C(x) = -27x² + 51000x + 20433

Function defining the revenue generated,

R(x) = -36x²+ 303000x

Since, Profit to the company = Revenue - Cost

= R(x) - C(x)

P(x) = -36x² + 303000x - (-27x² + 51000x + 20433)

= -36x² + 27x² + 303000x - 51000x - 20433

P(x) = -9x² + 252000x - 20433

To maximize the profit,

P'(x) = -18x + 252000 [Derivative of the function P(x)]

P'(x) = 0

-18x + 252000 = 0

18x = 252000

x = 14000

Therefore, for the maximum profit company has to produce and sell 14000 phones.