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.

Facility Annual Usage (people) Acres Cost ($) Priority Rugby fields 4,700 7 75,000 3 Football fields 12,500 12 180,000 2 Soccer fields 32,000 20 350,000 1 Dog park 7,500 6 45,000 3 Playground 41,000 3 120,000 2 Walking/running trails 47,000 25 80,000 1 Softball fields 23,000 5 115,000 2 Baseball fields 16,000 8 210,000 3

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 these facilities?

 LO.1