Question

An apartment complex on Ferenginar with 250 units currently has 170 occupants. The current rent for a unit is 510 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 1.5 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".

Answer 1

Let x = # of rent bumps

revenue = # occupants * rent per unit occupied
revenue = (170 - x) * ( 510 + 1.5*x)

in our problem, revenue (the money streaming in)
is the same as the profit, since no cost is given in the problem.

profit = (170 - x) * ( 510 + 1.5*x)
to maximize this we use the derivative

Answer 2

Answer:

Let x = # of rent bumps

revenue = # occupants * rent per unit occupied

revenue = (170 - x) * ( 510 + 1.5*x)

in our problem, revenue (the money streaming in)

is the same as the profit, since no cost is given in the problem.

profit = (170 - x) * ( 510 + 1.5*x)

to maximize this we use the derivative

To solve for x

we have to take the derivative

first expand it

p = (170 - x) * ( 510 + 1.5*x)

p(x) = (170 - x) * ( 510 + 1.5*x)

p(x) = -1.5*x^2 - 255*x + 86700

If you plot a gragh for the above equation you would have:

From the graph x = -80

So to calculate the max profit;

our recommendation is to lower rent price (by 1.5 latinums) 80 times, or

510 + 1.5 (-80) = 390.0

the maximum profit occurs when rent price is 390 dollars

Hope this helps. Thanks