Posted by **Melissa** on Monday, October 17, 2011 at 10:31pm.

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

- Math( help please ! ) -
**Reiny**, Tuesday, October 18, 2011 at 12:00am
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

- Math( help please ! ) -
**Sharlene**, Sunday, July 7, 2013 at 5:11pm
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

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