REAL ESTATE. Atlantic Standard Homes is developing 20 acres in a new community in the Florida Keys. There are four models it can build on each lot, and Atlantic Standard must satisfy three...

REAL ESTATE. Atlantic Standard Homes is developing 20 acres in a new community in the Florida Keys. There are four models it can build on each lot, and Atlantic Standard must satisfy three requirements: at least 40 are to be one story; at least 50 are to have three or more bedrooms; and there are to be at least 1 0 of each model. Atlantic Standard estimates the following gross profits:

a. Formulate the problem as an integer linear programming model and solve for Atlantic Standard’s optimal production of homes in this community.

 b. If the variables had not been restricted to be integers, the optimal linear programming solution gives X, = 30, X2 = 10, X, = 35.45, X4 = 10. Round this solution to an integer point. Is is feasible? How much lower is the optimal profit of the rounded solution than the optimal integer solution found in part (a)?

 c. Assume that a minimum of 12 homes must be built for at least three of the four models. Using four additional binary variables and five additional constraints, modify the model to reflect this new condition and solve for the new optimal distribution of homes for the Atlantic Standard project.