A real estate company owns 120 apartments which are fully occupied when the rent is $800 per month. Analytics indicate that for each $40 increase in rent, 5 apartments will become unoccupied. What rent should be charged in order to obtain the largest gross income?

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  $880

Step-by-step explanation:

If r is the rent charged, then the number of $40 increments of increase will be ...

  (r -800)/40

and the number of occupied apartments will be ...

  120 -5(r -800)/40

The gross income (g) will be the number of apartments times the rent charged, or ...

  g = r×(120 -5(r -800)/40) = (1/8)r(1760 -r)

The equation describes a parabola with zeros at r=0 and r=1760. The vertex will be on the line of symmetry, halfway between those zeros. The maximum gross income will be had when the rent is 1760/2 = 880.

$880 should be charged for rent to maximize gross income.

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