   Chapter 9.7, Problem 36E ### 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

# Revenue Suppose that the revenue function for a certain product is given by R ( x ) = 15 ( 2 x + 1 ) − 1 + 30 x − 15 where x is in thousands of units and R is in thousands of dollars.(a) Find the marginal revenue when 2000 units are sold.(b) How is revenue changing when 2000 units are sold?

(a)

To determine

To calculate: The marginal revenue when 2000 units of a certain product are sold.

Explanation

Given Information:

The revenue function for a product yields revenue which can be represented in the form of the function,

R(x)=15(2x+1)1+30x15

Here x is the units in thousand and R is in thousands of dollars.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

The derivative of a constant value, k, is

ddx(k)=0

According to the property of differentiation, if a function is of the form y=un, where u=g(x),

dydx=nun1dudx

Calculation:

Consider the provided revenue function,

R(x)=15(2x+1)1+30x15

The marginal revenue function is found by differentiating the revenue function with respect to x.

Consider (2x+1) to be u,

R(x)=15u1+30x15

Differentiate both sides with respect to x,

R(x)=ddx(15u1+30x15)=15ddx(u1)+ddx(30x)ddx(15)=15ddx(u1)+30(ddxx)ddx(15)

Simplify

(b)

To determine

How the revenue changes for the product when 2000 units are sold.

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