Question

The manager of big box store has found that if the price of a pillow is p(x) = 95 - x 8 , then x pillows will be sold. The expression for the total revenue from the sale of x pillows is R(x) = 95x - x 2 8 . Find the number of pillows that will produce maximum revenue.

Answer 1

Answer:the number of pillows that will produce maximum revenue is 380 pillows

Explanation:

The expression for the total revenue from the sale of x pillows is R(x) = 95x - x^2/8.

This is the revenue function The first step is to determine the first derivative of the revenue function. It becomes

R'(x) = 95 - 2x/8

R'(x) = 95 - x/4

The maximum value of a given function occurs when the derivative equals zero. Therefore

0 = 95 - x/4

x/4 = 95

x = 95 × 4 = 380

Answer 2

380

Explanation:

The revenue function is given by:

`R(x) = 95x- (x^2)/(8)`

Revenue will be maximized at the output (number of pillows sold) which yields a value of zero to the derivate of the revenue function:

`(dR(x))/(dx) = 0\\R'(x)=0 = 95- (2x)/(8)\\x=95*4\\x=380`

Revenue will be maximized when 380 pillows are sold.