The Stinson County Parks Department surveyed residents and found that there is a need for 7 gyms, 10 athletic fields, 8 tennis courts, and 12 swimming pools in the six towns that make up the county. The department has a budget of $600,000 and 50 acres of land for construction (although more land could be located if necessary). The information about each type of facility is given below: Facility Cost ($) Required Acres Expected Usage (people/week) Gymnasium 80,000 4 1,500 Athletic Field 24,000 8 3,000 Tennis Court 15,000 3 500 Swimming Pool 40,000 5 1,000 The Parks Department has determined the following goals, listed in order of their priority. a. Spend all of the budget. The current allocation comes from a federal grant, so any amount not spent must be returned and the federal government can reduce the size of future grants correspondingly. b. Have at least 20,000 residents use the recreation facilities each week. c. Avoid having to locate more land than the original 50 acres. d. Meet the residents’ demands. (Use “Expected Usage” as the weights for each type of facility) Determine how many of each type of facility should be constructed to best achieve Stinson County’s goals.