Math( help please ! )
posted by Melissa on .
The profit p(x) of a cosmetics company , in thousands of dollars,is given by p(x)=5x^2+400x2550, 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

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 
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