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The manager of a 100 unit apartment complex knows from experience that all units will be occupied if the rent is $500 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue?

  • Calculus -

    Income= rent(100-1/10*(rent-500)

    d I/drent= (100-rent/10+50)-rent(1/10)=0

    150=2/10 rent
    rent= 750
    check that

  • Calculus -

    checking : assume 750 rent, 760 rent, and 740 rent

    rent units income
    750 75 56,250
    740 76 56,240
    760 74 56240
    calculus is awesome

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