A real estate developer is planning a new mini apartment complex.

Three types of units can be built: one-bedroom apartments, two-bedroom apartments, and three-bedroom apartments.

Each one-bedroom apartment requires 700 square feet; each two-bedroom apartment requires 800 square feet; and each three-bedroom apartment requires 1,200 square feet.
The developer wants to keep a mix of apartment types in the complex. He believes that the number of one-bedroom apartments should be at least 15% of the total number of apartments. However three-bedroom apartments should not be more than 30% of the total number of apartments.

Local zoning laws do not allow the developer to build more than 42 units in this particular building location, and restrict the building to a maximum of 36,000 square feet.

Market studies show that one-bedrooms rent for $825 per month, two-bedrooms for $1,225 per month, and three-bedrooms for $1,775 per month.

a) Determine the constraint for square feet.

b) Determine the constraint for the number of total units.

c) Determine the constraint for one-bedroom apartments.

d) Determine the objective function.