1.A real estate company owns 180 apartments, whichare fully occupied when the re

Question

1.A real estate company owns 180 apartments, whichare fully occupied when the rent is $300 per month. The companyestimates that for each $10 increase in rent, 5 apartmentswill become unoccupied. What rent should be charged to obtainthe largest gross income?

2.An oil field contains 8 wells, which produce a totalof 1600 barrels of oil per day. For each additional well that isdrilled, the average production per well decrease by 10 barrelsper day. How many additional well should be drilled to obtainthe maximum amount of oil per day?

Explanation / Answer

1.total income= rent* appartment occupied

=(300+ n*10) (180-5*n)= 54000+300n-50n2

for maximum income, derivative fo income function=0

300-100n=0

n=3

so rent = 300+ n*10= $330

2. total oil output = total wells* no of barrels

=(8+n)(1600-n*10)

=(12800+1600n-80n-10n2)

for maximum output oil output function's derivative should be =0

derivative=(1600-80-20n)=0

n=76

therefore, 76 new wells

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