Chapter 9.9, Problem 6E

### 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 that in a monopoly market, the demand function for a product is given by p   = 160   −  0 .1 x where x is the number of units and p is the price in dollars.(a) Find the total revenue from the sale of 500 units.(b) Find and interpret the marginal revenue at 500 units.(c) Is more revenue expected from the 501st unit sold or from the 701st? Explain.

(a)

To determine

To calculate: The total revenue generated by selling 500units If the demand function for the product is represented by p=1600.1x where, x represents the number of unit sold and p represents the price (in dollar).

Explanation

Given information:

The provided demand function for the product is represented by p=160âˆ’0.1x where, x represents the number of unit sold and p represents the price (in dollar).

Formula used:

The total revenue for selling x unit of product is given by:

R(x)=pâ‹…x

Where R(x)â€‰andâ€‰p(x) are total revenue function and total demand function.

Calculation:

Consider the provided demand function,

p=160âˆ’0.1x

Since, x represents the number of unit sold that is 500 and p represents the demand function.

Therefore, apply the formula of total revenue that is, R(x)=pâ‹…x,

Now, substitute p=160âˆ’0.1x in the above formula,

Thus,

R(x)=(160âˆ’0

(b)

To determine

To calculate: The value of marginal revenue generated by selling 500units and also interpret the result, If the demand function for the product is represented by p=1600.1x where, x represents the number of unit sold and p represents the price (in dollar).

(c)

To determine

Whether the value of expected revenue generated by selling 501st units is more or 701st, If the demand function for the product is represented by p=1600.1x where, x represents the number of unit sold and p represents the price (in dollar).

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