# What rent should the manager charge to maximize revenue?

• Neil6790
In summary, the manager should charge a rent of $400 per month in order to maximize revenue. The revenue function can be represented as R(x) = 90x - (x-400)^2/10. To find the maximum value of the revenue, the derivative can be set equal to 0 or the vertex can be found by completing the square. Neil6790 The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 400 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue? All I know is that 90 units will give me$36000

What do I have to do after? I am so stuck on this problem I have no idea what to do.

Neil6790 said:
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 400 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. What rent should the manager charge to maximize revenue?

All I know is that 90 units will give me $36000 What do I have to do after? I am so stuck on this problem I have no idea what to do. OK, so R(90) = 90* 400 = 36000. How about R(89)? R(85)? R(91)? R(100)? More generally, what is R(x), where x represents the number of units that are occupied? In order to maximize the revenue function, you first need a revenue function. Neil6790 said: The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 400 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 10 dollar increase in rent. Similarly, one additional unit will be occupied for each 10 dollar decrease in rent. So the number of units, u, rented if the rent is r is 90- the number of 10 dollar increases in rent over 400. The increase is r- 400 and the number of 10 dollar increases in that is (r-400)/10. The number of units rented if the rent is r dollas per mont is u= 90- (r-400)/10 What rent should the manager charge to maximize revenue? All I know is that 90 units will give me$36000

What do I have to do after? I am so stuck on this problem I have no idea what to do.
Find the number of units rented if the rent is r. That's what I gave above. Find the revenue in that case: multiply the number of units rented times r.

Find the maximum value of that revenue. You can do it by setting the derivative equal to 0 or, since this is a quadratic, by completing the square to find the vertex.

## 1. What factors should be considered when determining the rent to maximize revenue?

Some factors that should be considered are the location of the property, the current market demand, the amenities and features of the property, and the expenses associated with maintaining the property.

## 2. How does the location of the property affect the rent price?

The location of the property is a major factor in determining the rent price as it can greatly impact the demand for the property. Properties in desirable locations with good access to transportation, amenities, and job opportunities can command higher rent prices.

## 3. Is it better to charge a higher rent or a lower rent to maximize revenue?

This ultimately depends on the market demand and the competition in the area. In some cases, charging a higher rent can result in a lower vacancy rate and ultimately lead to higher revenue. However, in a highly competitive market, charging a lower rent may be necessary to attract tenants and maintain occupancy rates.

## 4. How can amenities and features of the property affect the rent price?

Amenities and features such as parking, laundry facilities, and upgraded appliances can increase the desirability of a property and justify a higher rent price. However, it is important to consider the cost of providing these amenities and ensure that the rent price is still competitive in the market.

## 5. Should the expenses associated with maintaining the property be factored into the rent price?

Yes, it is important to consider the expenses associated with maintaining the property when determining the rent price. These expenses include property taxes, insurance, maintenance and repairs, and any other operational costs. If the rent does not cover these expenses, it may result in a loss of revenue for the manager.

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