help with calc please !?

Question

The profit function for a computer company is given by 𝑃(𝑥)=−𝑥2+30𝑥−25 where 𝑥 is the number of units produced (in thousands) and the profit is in thousand of dollars.

a) Determine how many (thousands of) units must be produced to yield maximum profit. Determine the maximum profit.

b)  Determine how many units should be produced for a profit of at least 40 thousand.

Answer 1

P(x) = -x^2 + 30x - 25

derive

P'(x) = -2x + 30

set to 0 and solve

-2x + 30 = 0

-2x = -30

x = 15

15000 units for max profit

40 = -x^2 + 30x - 25

x^2 - 30x + 65 = 0

x = 2.155 or 27.845

2155 or 27845 units