The profit p(x) of a cosmetics company , in thousands of dollars . is given by p(x) =-5t^2=400x-2550, where x is the amount spent on advertising in thousands of dollars
a) determine the maximum profit the company can make
b) dtermine the amount spent on advertising that will result in the maximum profit
c) what amount must be spent on advertising to obtain a profit of at least $ 4 000 000
2 answers
Your equation makes no sense, make sure you read what you typed before posting.
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
-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
3 answers