Answer :
Answer:
$732
Step-by-step explanation:
Given
[tex]y \to profit[/tex]
[tex]x \to widgets[/tex]
[tex]y = -x^2 + 64x - 292[/tex]
Required
The maximum profit
First, we calculate the maximum amount of widgets that can be sold using:
[tex]x = -\frac{b}{2a}[/tex]
Where:
[tex]a = -1; b = 64; x = -292[/tex]
So, we have:
[tex]x = -\frac{64}{2 * -1}[/tex]
[tex]x = -\frac{64}{-2}[/tex]
[tex]x = -(-32)[/tex]
[tex]x = 32[/tex]
The maximum profit is:
[tex]y = -x^2 + 64x - 292[/tex]
[tex]y = -(32)^2 + 64 * 32 - 292[/tex]
Using a calculator, we have:
[tex]y = 732[/tex]