Answer:
x = 14000
Step-by-step 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.
