An apartment complex on Ferenginar with 250 units currently has 193 occupants. The current rent for a unit is 965 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 2.5 slips of Latinum. What should be our recommendation for the optimal rent?The equation I got was ( 193 − x ) ⋅ ( 965 + 2.5 x ). I tried to maximize it and got x = − 96.5. The optimal rent is 965 + 2.5 ( − 96.5 ) = 723.75.This answer is not correct? Where did I make a mistake Thanks

Question

An apartment complex on Ferenginar with 250 units currently has 193 occupants. The current rent for a unit is 965 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 2.5 slips of Latinum. What should be our recommendation for the optimal rent?The equation I got was   (  193  −  x  )  ⋅  (  965  +  2.5  x  ). I tried to maximize it and got   x  =  −  96.5. The optimal rent is   965  +  2.5  (  −  96.5  )  =  723.75.This answer is not correct? Where did I make a mistake Thanks

Percyaehyq · Accepted Answer

You did nothing wrong!Notice that the equation of the total rent with respect to   x is a parabola. That means as   x goes from 0 to −96.5, the total rent is increasing. However, our maximum occupancy is 250 residents, so the rent is maximized at   x  =  −  57.

An apartment complex on Ferenginar with 250 units currently has 193 occupants. The current rent for

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