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# Help

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1 Any help is appreciated :)

Mar 23, 2018

### 1+0 Answers

#1
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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   Mar 23, 2018