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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 Suppose the total revenue function for a blender is

R ( x ) = 36 x  -  0.01 x 2 dollars where x is the number of units sold.

(a) What function gives the marginal revenue?

(b) What is the marginal revenue when 600 units are sold, and what does it mean?

(c) What is the marginal revenue when 2000 units are sold, and what does it mean?

(d) What is the marginal revenue when 1800 units are sold, and what does it mean?

(a)

To determine

To calculate: The function that gives the marginal revenue when the revenue function is given as R(x)=36x0.01x2.

Here x is the number of units sold.

Explanation

Given Information:

The revenue function is given as;

R(x)=36x0.01x2,

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:

The revenue function is given as;

R(x)=36x0.01x2

Here x is the number of units sold.

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

f(x+h)=36(x+h)0.01(x+h)2=36x+36h(0

(b)

To determine

To calculate: The marginal revenue when 600 units are sold and its meaning. The revenue function is given as

R(x)=36x0.01x2

Here x is the number of units sold.

(c)

To determine

To calculate: The marginal revenue when 2000 units are sold and its meaning. The revenue function is given as R(x)=36x0.01x2. Here x is the number of units sold.

(d)

To determine

To calculate: The marginal revenue when 1800 units are sold and its meaning. The revenue function is given as R(x)=36x0.01x2. Here x is the number of units sold.

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