Assesment $5-$ Problem $3$

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 $30035,0004$

Tennis center $9010,0004$

Athletic field $40025,0007$

Gymnasium $15095,0003\mathrm{.}5$

The community has a $$125,000$ construction budget and $15$ 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.