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+78x-543

for 50 points

Answer 1

978

Explanation:

This is an inverted parabola.

The maximum value occurs at x exactly in between the 2 zeros of the function.

y = -x^2 + 78x - 543

-x^2 + 78x - 543 = 0

x^2 - 78x + 543 = 0

x = [-(-78) ± √[(-78)^2 - 4(1)(543)]/[2(1)]

x = [78 ± √(6084 - 2172)]/2

x = 70.272 or x = 7.727

Midpoint of the zeros:

(70.272 + 7.727)/2 = 39

Maximum profit occurs at x = 39.

f(39) = -(39)^2 + 78(39) - 543

f(39) = 978

Maximum profit is 978.