Question

How many patterns my cell each month to the maximum profit to attain maximum profit they Maisel blank patterns what is the maximum profit the most profit is blank dollars

Answer 1

The given polynomial is

`p(x)=-0.002x^2+2.5x-600`

Differentiate with respect to x, we get

`p^(\prime)(x)=2(-0.002)x+2.5`

`p^(\prime)(x)=-0.002x+2.5`

Equate this to zero, we get

`-0.004x+2.5=0`

`-0.004x=-2.5`

`0.004x=2.5`

multiply by 1000 on both sides, we get

`0.004x*1000=2.5*1000`

`4x=2500`

`x=(2500)/(4)=625`

Hence they must sell 625 patterns to attain maximum profit.

Substitute x=625 in the given equation p(x), we get

`P(625)=-0.002(625)^2+2.5(625)-600`

`=-0.002*390625+2.5*625-600`

`=-781.25+1562.5-600`
`P(625)=181.25`

Hence the maximum profit is $ 181.25.