The town of Hillsboro recently purchased a 55-acre tract of farm land, and it has $550,000 budgeted to develop recreational facilities. The impetus for the purchase was the need for more soccer fields to meet the increasing demand of youth soccer in the area. However, once the land was purchased, a number of other interest groups began to lobby the town council to develop other recreational facilities including rugby, football, softball, and baseball fields, plus walking and running trails, a children's playground, and a dog park. The following table shows the amount of acreage required by each project, 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.

a. Formulate and solve a linear programming model that will maximize annual usage and achieve an average priority level of no more than 1.75.
b. Reformulate the model such that the objective is to achieve the minimum average priority level while achieving an annual usage of at least 120,000.
c. What combination of facilities will use the maximum acreage available without exceeding the budget and achieving an average priority level of no more than 1.75? What is the annual usage with thesefacilities?

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Facility Annual Usage (people Acres Cost (S) Priority 7 75,000 3 12 80,000 2 20 350,000 Rugby fields Football fields Soccer fields Dog park Playground Walking/running trail:s Softball fields Baseball fields 4,700 12,500 32,000 7,500 41,000 47,000 23,000 16,000 6 45000 3 3 120,000 2 80,000 5 115,000 2 8 210,000 3 25