Question

A company sells widgets. The amount of profit , ymade by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find the maximum amount of profit the company can make, to the nearest Dollar.

y=-x^2+64x-292

Answer 1

$732

Explanation:

Given

`y \to profit`

`x \to widgets`

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

Required

The maximum profit

First, we calculate the maximum amount of widgets that can be sold using:

`x = -(b)/(2a)`

Where:

`a = -1; b = 64; x = -292`

So, we have:

`x = -(64)/(2 * -1)`

`x = -(64)/(-2)`

`x = -(-32)`

`x = 32`

The maximum profit is:

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

`y = -(32)^2 + 64 * 32 - 292`

Using a calculator, we have:

`y = 732`