   Chapter 9.6, Problem 41E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Pricing and sales Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit (in dollars) of the product according to y =   32 ( 3 p +   1 ) − 2 / 5 ,     p   > 0 (a) What is the rate of change in sales volume when the price is $21?(b) Interpret your answer to part (a). (a) To determine To calculate: The rate of change of sales volume when the price is$21. Suppose that the weekly sales volume y (in thousands of dollars) depends on the price per unit (in dollars) of the product according to y=32(3p+1)2/5,p>0.

Explanation

Given Information:

The weekly sales volume y (in thousands of dollars) depends on the price per unit (in dollars) of the product according to y=32(3p+1)2/5,p>0. Also, the price is $21. Formula used: The power rule of differentiation, ddxxn=nxn1 Calculation: Consider the provided function, y=32(3p+1)2/5 Consider (3p+1) to be u, y=32u2/5 Differentiate both sides with respect to p, dydp=ddp(32u2/5) Simplify using the power rule, dydp=3225u251dudp=645u7/5dudp Substitute (3p+1) for u, dydp=645( (b) To determine The interpretation of the rate of change in sales volume when the price is$21. The weekly sales volume y (in thousands of dollars) depends on the price per unit (in dollars) of the product according to y=32(3p+1)2/5,p>0.

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