Question

An apartment complex on Ferenginar with 250 units currently has 223 occupants. The current rent for a unit is 892 slips of Gold-Pressed Latinum. The owner of the complex knows from experience that he loses one occupant every time he raises the rent by 2 slips of Latinum. Since "profit is its own reward", the owner wants to maximize his profit so he asks for our help, even though he knows that "free advice is seldom cheap". What should be our recommendation for the optimal rent?

Answer 1

Answer:

Step-by-step explanation:

Given data

Total units = 250

Current occupants = 223

Rent per unit = 892 slips of Gold-Pressed latinum

Current rent = 892 x 223 =198,916 slips of Gold-Pressed latinum

After increase in the rent, then the rent function becomes

Let us conside 'y' is increased in amount of rent

Then occupants left will be [223 - y]

Rent = [892 + 2y][223 - y] = R[y]

To maximize rent =

$\frac{dR}{dy}=0\\=2(223-y)-(892+2y)=0\\=446-2y-892-2y=0\\=-446-4y=0\\y=\frac{-446}{4}=-111.5$

Since 'y' comes in negative, the owner must decrease his rent to maximixe profit.

Since there are only 250 units available;

$y=-250+223=-27\\\\maximum \,profit =[892+2(-27)][223+27]\\=838 * 250\\=838\,for\,250\,units$

Optimal rent - 838 slips of Gold-Pressed latinum