Chapter 9.5, Problem 42E

### 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

# Revenue The revenue (in dollars) from the sale of x units of a product is given by R ( x ) = 3000 2 x + 2 + 80 x − 1500 Find the marginal revenue when 149 units are sold. Interpret your result.

To determine

To calculate: The marginal revenue if the revenue (in dollars) from the sale of x units of a product is given by R(x)=(3000)(2x+2)+80x1500 at 149 units.

Explanation

Given Information:

The provided equation is R(x)=(3000)(2x+2)+80xâˆ’1500.

Formula Used:

As per the quotient rule, if two functions are given in the form f(x)g(x), then the derivative is given as:

ddx(fg)=fâ€²â‹…gâˆ’gâ€²â‹…fg2.

The marginal revenue can be determined by the first derivative of the equation.

If a function is a sum of many functions, then the derivative is as follows:

fâ€²(x)=f1â€²(x)+f2â€²(x).

Calculation:

Consider the provided equation R(x)=(3000)(2x+2)+80xâˆ’1500.

In order to take out the revenue from the sale of the next unit, the following needs to be done,

The derivative of the second function is,

f2(x)=80xf2â€²(x)=80dxdx=80

The derivative of the third function is,

f3(x)=1500f3â€²(x)=ddx(1500)=0

The value of the first function is:

In the equation (3000)(2x+2), the value of,

f(x)=(3000)

And

g(x)=(2x+2)

Apply the quotient rule of the equation,

ddx(fg)=ddx(3000)â‹…(2x+2)âˆ’ddx(2x+2)â‹…(3000)(2x+2)2

Evaluate the equation further,

ddx(fg)=(ddx(3000))

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