A Small Town Wants to Build Some New Recreational Facilities

Essay

A small town wants to build some new recreational facilities. The proposed facilities include a swimming pool, recreation center, basketball court and baseball field. The town council wants to provide the facilities which will be used by the most people, but faces budget and land limitations. The town has $400,000 and 14 acres of land. The pool requires locker facilities which would be in the recreation center, so if the swimming pool is built the recreation center must also be built. Also the council has only enough flat land to build the basketball court or the baseball field. The daily usage and cost of the facilities (in $1,000) are shown below.
Formulate the ILP for this problem.
$$\begin{array} { c l c c c } \text { Variable } & \text { Facility } & \text { Usage } & \text { Cost ( \$1,000) } & \text { Land } \\\hline \mathbf { X } _ { 1 } & \text { Swimming pool } & 400 & 100 & 2 \\\mathbf { X } _ { \mathbf { 2 } } & \text { Recreation center } & 500 & 200 & 3 \\\mathbf { X } _ { 3 } & \text { Basketball caut } & 300 & 150 & 4 \\\mathbf { X } _ { 4 } & \text { Baseball Eield } & 200 & 100 & 5\end{array}$$