The company also thinks that its regular and

luxury customers are two very distinct groups.

In particular, Stargrove thinks that there will be no switching of regular customers

to luxury apartments or of the luxury customers to regular apartments.

The regular customers will not be able to afford a luxury apartment and

luxury customers will not settle for a regular apartment.

This assumptions will help Stargrove to calculate how many apartments of

each kind it will sell during the next year for

any combination of the demand and the number of apartments it decides to build.

It will also help the company to calculate the number of apartments,

if any, it will have to sell to the real estate investor at the reduced profit.

For regular apartments, if Stargrove builds R of them, and

the demand for the regular apartments turns out to be DR,

it can calculate both the numbers of apartments sold at the high profit

of $500,000 and at the low profit of $100,000.

For the high profit sales, Stargrove cannot sell more than what it builds, R.

And they cannot sell more than what's demanded, that's DR.

So, it will sell the minimum of the two numbers.

For example, if Stargrove builds 96 regular apartments,

that's 12 regular floors with 8 apartments on each floor, and

the number of buyers of regular apartments turns out to be 90.

The number of high profit sales the company will

make is minimum of (96, 90) = 90.

If on the other hand, the company builds 96 regular apartments and

the number of potential buyers turns out to be 100,

Stargrove will manage to sell 96, which is the minimum of 96 and 100.

The number of the regular apartments that the company will have to sell

at the low profit value, is the difference between what it builds R and

what it sells at the high profit value, which is the minimum of (R, Dr).

For example, if the company builds 96 regular apartments and the demand for

regular apartments is 90, then the company will have to sell 96- 90,

6 apartments to the real estate investor at low profit.