The brick oven bakery sells more loaves of bread when it reduces its price but then its profits change. The function y=-100 (x-1.75)) squared + 300 models the bakeries profits, in dollars, where x is the price of a load of bread in dollars. The bakery wants to. maximize its profits

The profit model is

y = - 100 (x - 1.75) ² + 300

where

x = price of a loaf of bread, dollars

y = profit, dollars

The profit function is a parabola with vertex at (1.75, 300). Because the curve is down due to the negative leading coefficient, the maximum value of y occurs at x = 1.75, and the maximum value is 300.

Alternatively, we can use calculus to obtain the result.

To maximize y, the derivative of y with respect to x should be zero.

That is,

-200 (x - 1.75) = 0 = > x = 1.75

To verify that x = 1.75 will make y a maximum, we require that the second derivative, evaluated at x = 1.75, is negative.

The second derivative is - 200, which verifies the maximum at x = 1.75

The maximum profit is

-100 (1.75 - 1.75) + 300 = $300

A graph of y versus x (shown below) confirms the result.