Case 1-Mix Binary Programming (5 points per part) A community council must decide which recreation facilities to construct in its community. Four new recreation facilities have been proposed a swimming pool, a tennis center, an athletic field and a gymnasium. The council wants to construct facilities that will maximize the expected daily usage by the residents of the community subject to land and cost limitations. The expected daily usage and cost and land requirements for each facility follow. Expected Usage Recreation Facility (people per day) Swimming pool 300 Tennis center Athletic field 400 Gymnasium 150 Land Requirement (Acres) 4 2 7 3 Cost ($) 35,000 10,000 25,000 90,000 90 The community has a $120.000 construction budget and 12 acres of land. Because the swimming pool and tennis center must be built on the same part of the land parcel, only one of these two facilities can be constructed. The council wants to know which of the recreation facilities to construct to maximize the expected daily usage. a. Write the Integer programming model for the above problem b. Solve the problem and give your answers