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.

1.) Formulate a capital budgeting problem that will maximize total annual usage.

**Please do not use computer software or Greek symbols. Show the variables written out. Please write out all the constraints (this is what I struggle with most).** Thanks

Note: Do NOT solve the problem after formulating.