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.

Recreation Facility	Expected Usage (people per day)	Cost ($)	Land Requirement (Acres)
Swimming pool	300	35,000	4
Tennis center	90	10,000	2
Athletic field	400	25,000	7
Gymnasium	150	90,000	3

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.

Write the Integer programming model for the above problem

Solve the problem and give your answers.

Please show the steps and formulas like =sumproduct( )