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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 9.9, Problem 7E
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Mathematical Applications for the ...

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

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 4CP
Problem 5CP
Problem 6CP
Problem 7CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
BuyFindarrow_forward

Mathematical Applications for the ...

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

MARGINAL REVENUE, COST, AND PROFIT

In 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)=36x−0.01x2.

Explanation

Given information:

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

R(x)=36x−0.01x2

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)=36x−0.01x2

Now to get the marginal revenue for this product, differentiate the revenue function R(x)=36x−0.01x2 with respect to x.

Therefore,

MR¯=R′(x)=36−0.02x

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)=36x−0.01x2.

(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)=36x−0.01x2.

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