Question

A company sells widgets. The amount of profit,y, made by the company is related to the selling price of each widgets,x, by the given equation. Using this equation, find out the maximum of profit the company can make, to the nearest dollar. Y=-x^2+64x-292

Answer 1

The maximum amount of profit is 32

Explanation:

Given

`y=-x^2+64x-292`

Required

Calculate the maximum amount of profit

A quadratic function is of the form

`y = ax^2 + bx + c`

and its maximum, y_max is calculated using:

`y_(max) = (-b)/(2a)`

So for
`y=-x^2+64x-292`

By comparison with
`y = ax^2 + bx + c`

We have that:

`a = -1`
`b = 64` and
`c = -292`

`y_(max) = (-64)/(2*-1)`

`y_(max) = (-64)/(-2)`

`y_(max) = 32`

Hence, the maximum amount of profit is 32