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=-8x^2+242x-1056

Answer 1

The equation is that of a parabola, meaning that the maximum (or sometimes minimum) is 1/2 the sum of the solutions found using the quadratic equation.

y = 0 for the 2 solutions to {-b +/- sqrt[b2 - 4ac]} / 2a, where a = -3, b = 152 and c = -1150 from the equation for y. Plug a, b and c into the quadratic formula to get x = 9.2571 and x = 41.4095 as the 2 solutions.

9.2571 + 41.4095 = 50.6666... and the midpoint is 25.3333...

When x = 25.3333..., y = 775.33333.....

To the nearest cent, x=25.33 results in a profit of 775.33.

When x=25.25, Y = 775.31

When x=25.4, Y = 775.32

These are both less than 775.33 when x = 25.33.