   Chapter 10, Problem 40RE ### 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 MMR II Extreme Bike Shop sells 54 of its most popular mountain bikes per month at a price of $1540 each. Market research indicates that MMR II could sell one more of these bikes if the price were$10 lower. At what selling price will MMR II maximize the revenue from these bikes?

To determine

To calculate: The value of selling price at which MMR II will maximize the revenue for these bikes if the bike ship sells 54 of its most popular mountain bikes per month at a price of $1540 each and the market research indicates that it could sell one more of these bikes for each$10 price reduction.

Explanation

Given Information:

The provided information is the bike ship sells 54 of its most popular mountain bikes per month at a price of $1540 each and the market research indicates that it could sell one more of these bikes for each$10 price reduction.

Formula Used:

As per the product rule, if two functions are given in the form f(x).g(x), then the derivative is given as:

ddx(f.g)=f.dgdx+g.dfdx

The total revenue R is equal to R=pq, where p is the revenue per unit and q is the number of units.

The revenue is maximized by finding the value of the variable at first derivative is equal to 0. Also checking by verifying that T(q)0 or not.

Calculation:

Consider the provided information,

The bike ship sells 54 of its most popular mountain bikes per month at a price of $1540 each and the market research indicates that it could sell one more of these bikes for each$10 price reduction.

Let x be the total number of units, then the revenue function is as follows:

R=(54+x)(154010x)

The derivative of the equation is as follows:

R=(54+x)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### What is the lowest score in the following distribution?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### Define applied research and basic research and identify examples of each.

Research Methods for the Behavioral Sciences (MindTap Course List)

#### 0 1 −∞ does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 