An office building containing 96,000 square ft of spaceis to be made into apartments.There at most 15 one bedroom units,each with 800 square ft of space. The remaining units each with 1200 square ft of space,will have two bedrooms. Rent for each one bedroom is $650 and the two bedrooms are $900.How many two bedroom apts should be built to maximize revenue? 70,15,80 or 120?

I chose 70

Right!

It's interesting that the company makes more money per square foot on the one-bedroom apartments than on the two-bedrooms.

To maximize revenue, we need to determine the optimal number of two-bedroom apartments that should be built.

Let's assume x represents the number of two-bedroom apartments to be built.
The number of one-bedroom apartments will be (15 - x).

The total square footage used by the one-bedroom apartments = (15 - x) * 800.
The total square footage used by the two-bedroom apartments = x * 1200.

Since the total square footage available is 96,000, we can set up an equation:
(15 - x) * 800 + x * 1200 = 96,000.

Expanding the equation:
12,000 - 800x + 1200x = 96,000.
400x = 84,000.
x = 210.

Therefore, the number of two-bedroom apartments that should be built to maximize revenue is 210.

To determine the number of two-bedroom apartments that should be built to maximize revenue, we need to consider the space available and the rental prices of each type of apartment.

Let's break down the information given:
- The office building contains 96,000 square feet of space.
- Each one-bedroom apartment has 800 square feet of space, and the rent is $650.
- Each two-bedroom apartment has 1200 square feet of space, and the rent is $900.

The first step is to calculate the maximum number of one-bedroom apartments that can be built. We divide the total available space by the space occupied by each one-bedroom unit:
96,000 square feet / 800 square feet per unit = 120 one-bedroom units (maximum)

Next, we need to calculate the remaining space available for two-bedroom apartments. To do this, multiply the number of one-bedroom units by the space they occupy and subtract it from the total available space:
(120 one-bedroom units * 800 square feet per unit) = 96,000 square feet - 96,000 square feet = 0 square feet (remaining)

The calculation above shows that if we build 120 one-bedroom apartments, there will be no space left for two-bedroom apartments.

Therefore, the correct answer is not 120. Let's check the other options:

- If we assume there are 80 two-bedroom apartments, each occupying 1200 square feet, the total space they occupy would be (80 * 1200) = 96,000 square feet. There would be no space left for one-bedroom apartments.
- If we assume there are 15 one-bedroom apartments, each occupying 800 square feet, the total space they occupy would be (15 * 800) = 12,000 square feet. The remaining space for two-bedroom apartments would be 96,000 square feet - 12,000 square feet = 84,000 square feet. If we divide this remaining space by the space occupied by each two-bedroom apartment, we get (84,000 square feet / 1200 square feet per unit) = 70 two-bedroom apartments.

So, based on the calculations, the answer is 70 two-bedroom apartments.

Therefore, you chose the correct answer: 70 two-bedroom apartments should be built to maximize revenue.