You have the following equation for the prfot y made by the company:
y = -4x² + 1375x - 6548
where x is the selling price of each widget.
In order to find the the price of widets to obtain the maximum profit, proceed as follow:
-find the derivative of y related to x:
y' = -4·2x + 1375 - 0
y' = -8x + 1375
- equal the previous result to zero and solve for x:
-8x + 1375 = 0 subtract both sides by 1375
-8x = -1375 divide by -8 both sides
x = -1375/(-8)
x = 171.88
Hence, the price of the widget should be $171.88 in order to the company can obtain the maximum profit
