Optimizing Rental Rates for Maximum Profit in a Real Estate Business

In summary, the real estate office manages 50 apartments in a downtown building with a rent of $900 per month when all units are occupied. For every $25 increase in rent, one unit becomes vacant. Each unit requires an average of $75 in maintenance and repairs per month. To maximize profits, the real estate office should charge a rent that results in a critical point when taking the derivative of the profit function and considering the interval for x.
  • #1
thomasrules
243
0

Homework Statement


A Real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, each unit requires $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits?

Homework Equations


The Attempt at a Solution



I really don't know how to go about this. what is the revenue? i mean obviously the price to rent x # of rooms rented. But yea...I really don't know

the Cost = 75x
 
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  • #2
get the profit function, which is the revenue minus the profit. then take the derivative and set it to zero to get your critical point, but don't forget to consider the interval for x, and show that you indeed get a maximum.
 

Related to Optimizing Rental Rates for Maximum Profit in a Real Estate Business

1. What is the importance of understanding rates of change in business?

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To calculate the rate of change, you need to determine the difference between the starting and ending values of a variable, and then divide that difference by the time interval between the two values. The formula for calculating the rate of change is: (Ending Value - Starting Value) / Time Interval.

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