Solve each problem.
-If the price charged for a bolt is $p$ cents, then $x$ thousand bolts will be sold in a certain hardware store, where $p=125-\frac{x}{14}$. How many bolts must be sold to maximize revenue?
A) 875 thousand bolts
B) 1750 thousand bolts
C) 875 bolts
D) 1750 bolts

Question

Quizplus · Accepted Answer

The revenue is given by $R=px=(125-\frac{x}{14})x=125x-\frac{x^2}{14}$. To maximize revenue, we take the derivative of $R$ with respect to $x$ and set it equal to 0:$$\frac{dR}{dx}=125-\frac{2x}{14}=0$$$$125=\frac{2x}{14}$$$$x=875$$Therefore, 875 thousand bolts must be sold to maximize revenue.

Solve Each Problem ppp Cents, Then xxx Thousand Bolts Will Be Sold in a Certain Hardware Store

Solve Each Problem $p$ Cents, Then $x$ Thousand Bolts Will Be Sold in a Certain Hardware Store