Chapter 9.5, Problem 44E

Mathematical Applications for the ...

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

Chapter
Section

Mathematical Applications for the ...

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

Revenue McRobert's Electronics sells 200 TVs per month at a price of $400 per unit. Market research indicates that the store can sell one additional TV for each$1 it reduces the price. In this case, the total revenue is R ( x ) =   ( 200   +   x ) ( 400   − x ) where x is the number of additional TVs beyond the 200. If the store sells a total of 250 TVs, find the marginal revenue. Interpret your result.

To determine

To calculate: The marginal revenue if store sells total of 250 TVs when McRobert’s Electronics sells 200 TVs per month at a price of $400 per unit if the store can sell one additional TV for each$1 it reduces the price.

The total revenue is given by the equation R(x)=(200+x).(400x).

Explanation

Given Information:

McRobert’s Electronics sells 200 TVs per month at a price of $400 per unit if the store can sell one additional TV for each$1 it reduces the price.

The provided revenue equation is R(x)=(200+x).(400x)

Formula Used:

If two functions are given in the form f(x)+g(x), then the derivative is given as:

ddx(f+g)=dfdx+dgdx

The marginal revenue of the function is the first derivative of the revenue function.

Calculation:

Consider the provided information is,

McRobert’s Electronics sells 200 TVs per month at a price of $400 per unit if the store can sell one additional TV for each$1 it reduces the price.

Consider the provided revenue equation is R(x)=(200+x).(400x)

Multiply the factors and rewrite the above equation as

R(x)=(200+x)

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