The manager of a 70 -unit apartment complex is trying to decide what rent to charge. Experience has shown that at a rent of all of the units
will be full. On average, one additional unit will be vacant for each increase in rent.
Answer parts (a) through (e) below.
The maximum revenue will happen when .
(Round to the nearest whole number as needed.)
(e) What is the maximum revenue?
The maximum revenue is .
(Round to the nearest whole number as needed.)

Ask by Reed Clark. in the United States

Dec 15,2024

Question

The manager of a 70 -unit apartment complex is trying to decide what rent to charge. Experience has shown that at a rent of all of the units
will be full. On average, one additional unit will be vacant for each increase in rent.
Answer parts (a) through (e) below.
The maximum revenue will happen when .
(Round to the nearest whole number as needed.)
(e) What is the maximum revenue?
The maximum revenue is .
(Round to the nearest whole number as needed.)

Ask by Reed Clark. in the United States

Dec 15,2024

UpStudy AI · Accepted Answer

Given:
- The manager of a 70-unit apartment complex is trying to decide what rent to charge.
- At a rent of $850, all of the units will be full.
- On average, one additional unit will be vacant for each $25 increase in rent.
- The maximum revenue will happen when $$ x = 18 $$.

Let's denote:
- $$ x $$ as the number of $25 increases in rent.
- $$ R $$ as the revenue.

The revenue function can be expressed as:
$$ R = (70 - x) \times (850 + 25x) $$

To find the maximum revenue, we need to find the value of $$ x $$ that maximizes the revenue function $$ R $$.

Given that the maximum revenue happens when $$ x = 18 $$, we can substitute this value into the revenue function to find the maximum revenue.

Substitute $$ x = 18 $$ into the revenue function:
$$ R = (70 - 18) \times (850 + 25 \times 18) $$

Now, we can calculate the maximum revenue.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(70-18\right)\left(850+25\times 18\right)$$
- step1: Subtract the numbers:
  $$52\left(850+25\times 18\right)$$
- step2: Multiply the numbers:
  $$52\left(850+450\right)$$
- step3: Add the numbers:
  $$52\times 1300$$
- step4: Multiply the numbers:
  $$67600$$
The maximum revenue is $67,600.
The maximum revenue is $67,600.

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