Hale Scheckelhoff & Matt Millman
Calculus 151
Optimizing Writing Project
Two calculus students purchase 100 residential units with hopes of selling the houses with rent at
$900 per month. At that price, every unit will be sold. As the rent increases (on a monthly basis
by X amount of dollars) the occupancy will decrease by X/10 residential units. However,
maintenance is also in the equation as an occupied unit has a maintenance cost of $100 per
month while an unoccupied unit has a maintenance cost of $20 per month. The owners wish to
know the amount of rent to maximize the net income from the residential units. This can be
solved with a demand and cost equation.
The equation for how many units are rented is:
0=(x/10)+100
The equation for the cost of the rent for the residential units is:
Y=((x/10)+100)(900+x)
These equations would work, but maintenance work is also required for each of rented and
unoccupied residential units. For an occupied residential unit the cost to maintain is $100 per
month and we can multiply that by the amount of units we have occupied. For unoccupied units
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 Fall '08
 Rollins
 Calculus, Optimization, Net Income, Harshad number, Fermat's theorem

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