Respuesta :
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
Answer:
Check the explanation
Explanation:
This is a question under Calculus (which is another segment of mathematics and it is utilized for understanding the changes between values that are related by a function. Calculus is used in a lot of diverse fields of study such as astronomy, physics, biology, economics, medicine, engineering and sociology).
The step by step solution to the above question can be seen in the attached image below:
