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.
