The manager of big box store has found that if the price of a pillow is $\mathrm { p } ( \mathrm { x } ) = 95 - \frac { \mathrm { x } } { 8 }$, then $\mathrm { x }$ pillows will be sold.
The expression for the total revenue from the sale of $x$ pillows is $R ( x ) = 95 x - \frac { x ^ { 2 } } { 8 }$. Find the number of pillows that will produce maximum revenue.
A) 360 pillows
B) 420 pillows
C) 760 pillows
D) 380 pillows

Question

Quizplus · Accepted Answer

To find the number of pillows that will produce maximum revenue, we differentiate the revenue function $R(x) = 95x - \frac{x^2}{8}$ with respect to $x$ and set the derivative equal to zero to find the critical points. The derivative of $R(x)$ is $R'(x) = 95 - \frac{x}{4}$. Setting $R'(x) = 0$ gives $95 = \frac{x}{4}$, which leads to $x = 380$. This is the number of pillows that will produce maximum revenue.

The Manager of Big Box Store Has Found That If p(x)=95−x8\mathrm { p } ( \mathrm { x } ) = 95 - \frac { \mathrm { x } } { 8 }p(x)=95−8x​

The Manager of Big Box Store Has Found That If $\mathrm { p } ( \mathrm { x } ) = 95 - \frac { \mathrm { x } } { 8 }$