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.

equation: y=−2x^2+145x−1051

Answer 1

The maximum amount of profit the company can make is of $1577.

Explanation:

The profit is given by the following equation:

`y = -2x^2 + 145x - 1051`

Which is a quadratic equation.

Maximum value of a quadratic function:

Suppose we have a quadratic function in the following format:

`y = ax^2 + bx + c, a < 0`

The maximum value of the function is given by:

`y_(MAX) = (-(b^2-4ac))/(4a)`

In this question, we have that:

`a = -2, b = 145, c = -1051`. So

`y_(MAX) = (-(b^2-4ac))/(4a)`

`y_(MAX) = (-(145^2-4(-2)(-1051)))/(4(-2))`

`y_(MAX) = 1577.125`

To the nearest dollar, $1577

The maximum amount of profit the company can make is of $1577.