Question

n your computer store you charge $1012 per computer sold. Your costs are given by the equation C(x) = 4x^2 + 4x - 80 where x is the number of computers sold. Find the maximum profit.

Answer 1

63568 dollars

Explanation:

Given that in your computer store you charge $1012 per computer sold. Your costs are given by the equation

`C(x) = 4x^2 + 4x - 80`

where x is the number of computers sold.

Revenue = sales price *no of computers sold

= 1012x

Profit = Revenue - cost

=
`1012x-( 4x^2 + 4x - 80)\\= 1008x-4x^2+80\\`

Use derivative test to find maximum profit

`C'(x) = 1008-8x \\C''(x)= -x<0`

Equate I derivative to 0

x= 128

i.e. if 128 computers are manufactured and sold profit wouldbemaximum

Profit maximum=
`1008(128)-4(128)^2+80\\=63568`