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Optimizing Writing Project

# Optimizing Writing Project - Hale Scheckelhoff Matt Millman...

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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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