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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

Marginal revenue The revenue function for a sound system is

R ( x )   =   300 x   x 2 dollars

where x denotes the number of units sold.

(a) What is the function that gives marginal revenue?

(b) What is the marginal revenue if 50 units are sold, and what does it mean?

(c) What is the marginal revenue if 200 units are sold, and what does it mean?

(d) What is the marginal revenue if 150 units are sold?

(e) As the number of units sold passes through 150, what happens to revenue?

(a)

To determine

To calculate: The function that gives the marginal revenue when the revenue function is given as R(x)=300xx2. Here x is the number of units sold.

Explanation

Given Information:

The revenue function is given as;

R(x)=300xx2

Here x is the number of units sold.

Formula used:

If a function f(x) is defined in the interval [x+h,x], then its derivative is given by the formula,

f(x)=limh0f(x+h)f(x)h

Calculation:

Consider the provided statement,

The revenue function is given as;

R(x)=300xx2

Here x is the number of units sold.

Substitute x=x+h in f(x) to get,

f(x+h)=300(x+h)(x+h)2<

(b)

To determine

To calculate: The marginal revenue when 50 units are sold. The revenue function is given as R(x)=300xx2.

Here x is the number of units sold.

(c)

To determine

To calculate: The marginal revenue when 200 units are sold. The revenue function is given as R(x)=300xx2.

Here x is the number of units sold.

(d)

To determine

To calculate: The marginal revenue when 150 units are sold. The revenue function is given as R(x)=300xx2. Here x is the number of units sold.

(e)

To determine

The change in revenue as number of units becomes greater than 150. The revenue function is given as R(x)=300xx2. Here x is the number of units sold.

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