   Chapter 10.3, Problem 33E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# A company handles an apartment building with 50 units. Experience has shown that if the rent for each of the units is $720 per month, all of the units will be filled, but 1 unit will become vacant for each$20 increase in this monthly rate. If the monthly cost of maintaining the apartment building is $12 per rented unit, what rent should be charged per month to maximize the profit? To determine To calculate: The rent should be charged per month to maximize the profit. To maintain the apartment building the monthly cost is$12 rented units.

Explanation

Given Information:

The provided information is:

The 50 units of an apartment building handle by the company. According to experience the rent for each unit is $720 per month and all the unit has filled but 1 unit can be vacant for$20 increase in the monthly Rate.

Formula Used:

The total profit function is:

P(x)=R(x)C(x)

Where R(x)&C(x) are total revenue function and total cost function.

Calculation:

Consider the given data.

If the monthly cost of maintaining the apartment building is \$12 rented units.

The total profit function is:

P(x)=R(x)C(x)

Where R(x)&C(x) are total revenue function and total cost function.

Let x be the number of vacant units.

The total profit function is:

P(x)=(720+20x)(50x)12(50x)P(x)=35400+292x20x2

Then, the total profit function is 35400+292x20x2.

Differentiate the above function with respect to x as:

P(x)=29240x

If x=7.3 then P'(x)=29240x will be,

P(x)=29240xP(7.3)=29240(7

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