Answer:
The maximum amount of profit is 32
Step-by-step explanation:
Given
[tex]y=-x^2+64x-292[/tex]
Required
Calculate the maximum amount of profit
A quadratic function is of the form
[tex]y = ax^2 + bx + c[/tex]
and its maximum, y_max is calculated using:
[tex]y_{max} = \frac{-b}{2a}[/tex]
So for [tex]y=-x^2+64x-292[/tex]
By comparison with [tex]y = ax^2 + bx + c[/tex]
We have that:
[tex]a = -1[/tex] [tex]b = 64[/tex] and [tex]c = -292[/tex]
[tex]y_{max} = \frac{-64}{2*-1}[/tex]
[tex]y_{max} = \frac{-64}{-2}[/tex]
[tex]y_{max} = 32[/tex]
Hence, the maximum amount of profit is 32
