+0  
 
-1
157
1
avatar+956 

 

Any help is appreciated :) 

Julius  Mar 23, 2018
 #1
avatar+92477 
+2

Call the number of $15 rent increases, x

 

So....

The number of apartments rented  can be expressed as  (100 - x)

The revenue  earned  per apartment  is   (800 + 15x)

 

The total revenue   is     Number of apartments rented  *  Revenue per apartment

The total maintenance cost is hazy....I'm taking it to mean $60 * number of apartments rented  (since unrented apartments shouldn't require any maintenance )

 

So.....the Total Profit per month is    Total Revenue per month  - Total Maintenance cost per month

 

So we have

 

P(x)  =  (100 - x)(800 + 15x)  -  (60)(100-x)

 

P(x)  =  (100 - x) (800 + 15x - 60 )

 

P(x) = (100 - x) (15x + 740 )

 

Which simplifies to

 

P(x)  =  -15x^2 + 760x + 74000

 

Take the derivative of this and set to 0

 

P'(x)  =  -30x + 760

 

-30x + 760  = 0

 

760  = 30x       divide both sides by 30

 

x  =  25.333   ≈  25  =   number of $15  increases

 

This  means that the max profit is made when about (100 - 25)  =  75  apartments are rented 

 

 

And the max profit is achieved when the rent per apartment  is  (800 + 15(25) )  ≈

 

$1125   per month

 

And the max revenue  is  about

 

  -15 (25)^2  + 760 (25)  + 74000  =  $83625

 

Note that if all 100 apartments were rented.....  x  = 0  ..... and he would only make ≈ $74000

 

 

 

cool cool cool

CPhill  Mar 23, 2018

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