Linear Programming: 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 850 square feet; and each three-bedroom apartment requires 1,250 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.