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Schach [20]
2 years ago
10

(1 pt) The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 420 dollars

per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 3 dollar increase in rent. Similarly, one additional unit will be occupied for each 3 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Business
1 answer:
klasskru [66]2 years ago
3 0

Answer:

Monthly rent of $345 would maximize revenue

Explanation:

Revenue = Price * Quantity

Quantity depends on price. We need to work out the relationship between price and quantity (that is, the demand function)

When the rent is $420, quantity demanded is 90 units:

When P = 420 we have Q = 90

Let x be the change in price. For every 3 dollar increase (decrease) in price demanded quantity will decrease (increase) 1 unit:

P = 420 + x (a) we have Q = 90 - x/3 (b)

To find the relationship between P and Q we seek to eliminate x.

Multiply both sides of (b) with 3 we have: 3Q = 270 - x (b')

From (a) and (b') we have: P + 3Q = 420 + x + 270 - x

=> P = 690 - 3Q

Revenue R = P * Q = (690 - 3Q) * Q = 690Q - 3Q^2

To find maximum set derivative of R to 0:

dR = 690 - 6Q = 0

=> Q = 690/6 = 115

To lease 115 the price should be P = 690 - 3Q = 690 - 3*115 = 345

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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

Learn more about the rent at brainly.com/question/2254034

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GrogVix [38]

both of the above are undermine the private sector.

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Read the sentence. French women influenced Enlightenment intellectuals, government officials, and the wealthy middle class by ho
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A salon is a group of personalities beneath one rooftop of an inspirational host, endured partially to tickle one another also slightly to improve the flavor and enhance the learning of the cooperators throughout the communication. Salons in the custom of the French literary including philosophical movements from the 17th and 18th centuries were moved on until as freshly as the 1920s in urban surroundings.

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When Coca-Cola focused on developing its soft-drink business but missed seeing the market for coffee bars and fresh-fruit-juice
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A. marketing myopia

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Why might a manager for a non-profit organization seem as concerned with his or her organization's financial well-being as a for
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c. Not-for-profit organizations need to make money to continue operating.

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Non-profit organisations mainly focus on meeting their set objectives for example ensuring education is provided to poor children, health services reach the less privileged in society, and so on.

On the other hand for profit organisations mainly focus on turning a profit for the benefit of the business owners.

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