Question

The manager of a 150-unit apartment complex knows from experience that all units will be occupied if the rent is $1000 per month. A market survey suggests that, on average, one additional unit will remain vacant for each $20 increase in rent. What rent should the manager charge to maximize revenue?.

Answer 1

The rent that the manager should charge to maximize revenue will be $2,000.

In business, a rent is known as the cost incurred by a business to utilize a property or location for an office, retail space, factory, or storage space.

Initially, to find revenue by coming up we can calculate with an equation below:

Revenue = Price × Revenue

Where, price = 1000 + 20x

Quantity = 150 - x

R(x) = (1000+20x) (150-x)

R(x) = 150000 - 1000x + 3000x - 20x²

R(x) = - 20x² + 2000x + 150000

To maximize the revenue, we calculate the derivative and set it to zero:

R(x) = - 20x² + 2000x + 150000

R(x) = -40x + 2000

-40x + 2000 = 0

40x = 2000

x = 50

After we find the amount of X, thus we determine the rent that the manager should  charge to maximize revenue

Price=$1000+20x

Price=$1000+20(50)

Price=$1,000 + 1,000

Price = $2,000

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