Question

The profit p(x) of a cosmetics company , in thousands of dollars,is given by p(x)=-5x^2+400x-2550, where x is the amount spent on advertising , in thousands of dollars

a) determine the max profit the company can make
b)Determine the amount spent on advertising that will result in the max profit
c)What amount must be spent on advertising to obtain a profit of at least $4 000 000

Answer 1

p(x) = -5x^2 + 400x - 2550

p'(x) = -10x + 400
= 0 for a max of p(x)
10x = 400
x = 40 -----> answer for b)

p(40) = -5(40^2) + 400(40) - 2550 = 5450 -- > a)

for c)
solve
4000 = -5x^2 + 400x - 2550

Answer 2

a. Complete the square.
-5x^2 + 400x - 2550
= -5(x^2 - 80x) - 2550
= -5(x^2 - 80x + 1600 - 1600) - 2550
= -5(x + 40)^2 + 8000 - 2550
= -5(x + 40)^2 + 5450
5450 x 1000 = $5,450,000
b. x = 40
40 x 1000 = $40000
c. Between $22 971 & 57 029

Answer 3

The profit of a cosmetics company, P= -5x^2+40x-20