Answer:
The rent that should be charged to maximize gross icome is $700.
Explanation:
The rent can be increased by $25 steps.
The rent equation can be written as,
Rent = 650 + 25x
The Apartments occupied will fall by 4 apartments everytime the rent is increased by $25.
The apartment occupancy equation can be written as,
Apparment occuoancy = 120 - 4x
Where, x is the number of times the rent is increased by $25.
The revenue will be,
Revenue = Rent * No of apartments occupied
Revenue = (650 + 25x) * (120 - 4x)
Solving the equation we get quadratic equation,
Revenue = 78000 - 2600x + 3000x - 100x²
0 = 78000 + 400x - 100x²
As we need the change, we need to take the derivative of this equation.
d/dx = 0 + 1 * 400x° - 2 * 100x
400 - 200x = 0
400 = 200x
400 / 200 = x
x = 2
Thus, the rent that should be charged to amximize gross income is,
Rent = 650 + 25 * (2) = $700 per apartment
The revenue at this rent will be,
Revenue = 700 * [120 - 4 * (2)] = $78400
