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=-13x^2+770x-6332

Answer 1

The maximum profit is 5070 dollars

Explanation:

The profit y is represented by a quadratic function.

The equation that we can use to find a maximum value of a quadratic function is:

Max_value = c - (b^2 / 4a)

Where a, b and c are the coefficients of the quadratic function (in our case: a = -13, b = 770, c = -6332)

So, using this equation, we have:

Max_value = -6332 - (770^2 / 4*(-13)) = -6332 - 592900/(-52)

Max_value = -6332 + 11401.92 = 5069.92

rounding to the nearest dollar, we have that the maximum profit is 5070 dollars.