Chapter 9.9, Problem 7E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 1-8, total revenue is in dollars and x is the number of units.Suppose the total revenue for a certain product is given by R ( x ) = 36 x −  0 .01 x 2 .(a) Graph the marginal revenue function for this product.(b) At what value of x will total revenue be maximized?(c) What is the maximum revenue?

(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)=36xâˆ’0.01x2

Formula used:

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

MRÂ¯=Râ€²(x)

Graph:

Consider the total revenue function,

R(x)=36xâˆ’0.01x2

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

Therefore,

MRÂ¯=Râ€²(x)=36âˆ’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)=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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