   Chapter 9.9, Problem 8E ### 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 4.(b) Determine the number of units that must be sold to maximize total revenue.(c) What is the maximum revenue?Suppose that the total revenue function for a commodity is R ( x ) = 25 x   − 0.05 x 2 .(a) Find R ( 50 ) and tell what it represents.(b) Find the marginal revenue function.(c) Find the marginal revenue at x = 50, and tell what it predicts about the sale of the next unit and the next 2 units.(d) Find R ( 51 ) − R ( 50 ) 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)=25x0.05x2.

Explanation

Given information:

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

R(x)=25x0.05x2

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)=25x0.05x2

Now to get the marginal revenue for this product, differentiate the revenue function R(x)=25x0.05x2 with respect to x.

Therefore,

MR¯=R(x)=250.1x

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)=25x0.05x2.

(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)=25x0.05x2.

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