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+90x-454

Answer 1

9514 1404 393

Answer:

$1571

Explanation:

If we assume that y is profit in dollars, the maximum value of y is revealed by a graph to be ...

ymax = $1571

The maximum profit the company can make is $1571 at a selling price of $45 each.

_____

The function can be written in vertex form as ...

y = -(x^2 -90x) -454

y = -(x^2 -90x +45^2) -454 +45^2

y = -(x -45)^2 +1571

Because the leading coefficient is negative, we know this vertex represents a maximum. (x, y) = (45, 1571) at the vertex. Maximum profit is $1571.