Question

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out the maximum amount of profit the company can make, to the nearest dollar. y=-x^2+62x-410

Answer 1

$551

Explanation:

Given the amount of profit, y, made by the company, is related to the selling price of each widget, x, by the equation y=-x^2+62x-410

The company make the maximum profit at when dy/dx = 0

dy/dx = -2x + 62

Since dy/dx = 0

0 = -2x + 62

2x = 62

x = 62/2

x = 31

substitute x = 31 into the expression y=-x^2+62x-410

y=-x^2+62x-410

y=-31^2+62(31)-410

y = -961+1922-410

y = 551

Hence the maximum profit the company can make is $551