   Chapter 9.9, Problem 7E ### 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

# MARGINAL REVENUE, COST, AND PROFITIn Problems 1-8, total revenue is in dollars and x is the number of units.(a) Graph the marginal revenue function from Problem 3.(b) At what value of x will total revenue be maximized for Problem 3.(c) What is the maximum revenue?Suppose that the total revenue function for a commodity is R =   36 x   −   0.01 x 2 .(a) Find R(100) and tell what it represents.(b) Find the marginal revenue function.(c) Find the marginal revenue at x = 100, and tell what it predicts about the sale of the next unit and the next 3 units.(d) Find R ( 101 )   − R ( 100 ) and explain what this value represents.

(a)

To determine

To graph: The marginal revenue function for the product If the total revenue for this product is represented by the function R(x)=36x0.01x2.

Explanation

Given information:

The provided total revenue for this product is represented by the function,

R(x)=36x0.01x2

Formula used:

The marginal revenue generated on a sale of x units of product is given by,

MR¯=R(x)

Graph:

Consider the total revenue function,

R(x)=36x0.01x2

Now to get the marginal revenue for this product, differentiate the revenue function R(x)=36x0.01x2 with respect to x.

Therefore,

MR¯=R(x)=360.02x

The graph of the functions can be made by using Ti-83 calculator follow the steps below as:

Step 1: Open Ti-83 calculator

(b)

To determine

To calculate: The value of x which provides the maximum total revenue, If the total revenue for this product is represented by the function R(x)=36x0.01x2.

(c)

To determine

To calculate: The value of the maximum revenue, If the total revenue for this product is represented by the function R(x)=36x0.01x2.

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