A real estate company recently purchased a 52 acre of farm land, and it has $435,000 budgeted to develop recreational facilities. They are considering the facilities for soccer fields, swimming pool, walking trails, and a children's playground to develop.

The following table shows the amount of acreage required by each facility, the annual expected usage for each facility, and the cost to construct each facility.

Also included is a priority designation determined by the town's recreation committee based on several public hearings and their perceptions of the critical need of each facility.

Facility           Annual Usage (people)             Acres           Cost ($)                Priority

Swimming pool                    22,500                               8            120,000                   2

Soccer fields            20,400                             20            100,000                   2

Playground              36,800                             14            140,000                   1

Walking trails         50,000                             18              95,000                   1

The total priority level cannot be more than 3. The company wants to select at least three facilities to develop.

Formulate a capital budgeting problem that will maximize total annual usage by determining:

(a) The decision variables.

(b) The objective function. What does it represent?

(c) All the constraints. What does each constraint represent?