Springmeadow Park Board is considering a new recreation complex with a variety of facilities. Expected costs (in thousands), space requirement (in square feet), and projected average usage figures are given in the table below. The department has a total of $1 million to spend specifically for the facilities. The building will have a maximum size of 20,000 square feet allocated to the indoor facilities listed below (thus this area excludes offices, lobbies, meeting rooms, etc.). In addition, there will be a maximum of 50,000 square feet of outdoor space available for these facilities. Councilman Bundy feels strongly that at most only one pool should be included in the complex. Councilwoman Simpson, whose daughter skates and son plays soccer, insists that if a baseball field is built then both a skating rink and soccer field must also be included in the park. If the park board wishes to maximize average usage of the complex, formulate the integer programming problem to determine which facilities should be included.
Facility Cost Space requirements Expected usage/day
Fitness Center (I) $200 2,000 60
Pool (I) 80 5,500 75
Pool (O) 65 7,200 40
Auditorium (I) 150 5,000 30
Gymnasium (I) 250 7,500 60
Tennis courts (O) 60 5,000 15
Baseball field (O) 90 25,000 35
Soccer fields (O) 80 25,000 44
Skating rink (I) 250 5,000 25
(I) indoor (O) outdoor