Profit-oriented Millard Construction is contemplating building a planned community with the help of federal funds. These funds are to be distributed only if Millard meets federal standards for low cost housing. There are three types of units -- houses, town-houses, and high rise condominiums. There are three styles each of the houses and town-houses -- low cost, standard, and deluxe. The high rise condominium will have only standard and deluxe models. Millard needs to determine the number of units of each type of housing for this community at this planning stage.

The amount of total ground area (including allowances for parking and green belts) per unit of each type is given in the following table:

The profit to Millard per unit is summarized in the following table:

Millard has 300,000 square feet for construction. To make the project "work",

Millard wants the area of Houses to occupy between 25% and 40% of the total area while the area of Condominiums only need to occupy between 10% to 30% of the total area complex be low cost units

1) Define your decision variables:

2) Write the objective function:

3) Write all constraints related to the problem:

Houses Town-houses Condominiums Ground Area (Sq. Ft.) Standard 2200 1800 1000 Low Cost 1800 780 Deluxe 3000 2230 1500 Houses Town-houses Condominiums Unit Profit ($1000's) Standard 12 12 9 Low Cost 5 6 X Deluxe 25 20 16