Question 2: Binary Programming (25 Points) The town of Hillsboro recently purchased a 55-acre tract of farm land, and it has $550,000 budgeted to develop recreational facilities. A number of interest groups began to lobby the town council to develop other recreational facilities including rugby, football, softball, and baseball fields, plus walking and running trails, a children's playground, and a dog park. Page 1 of 3 The following table shows the amount of acreage required by each project, the annual expected usage for each facility, and the cost to construct each facility. Also included is a priority designation determined by the town's recreation committee based on several public hearings and their perceptions of the critical need of each facility. Facility Annual Usage (People) Acres Cost ($) Priority Rugby field 4,700 75,000 Football field 12,500 12 180,000 N Soccer field 32,000 20 350,000 Dog Park 7,500 6 45,000 w Playground 41,000 3 120,000 N Walking/running trail 47,000 25 80,000 Softball field 23,000 115,000 W N - Baseball field 16,000 8 210,000 The town wants to build at least 3 facilities. Because the Rugby field can be used for football, soccer games, the town does not want to build more than one of those three fields. Due to the safety concern, the playground should not be built if the dog park is built. Moreover, if the softball field is built then the baseball field should be built as well. Formulate and solve a linear programming model that will maximize annual usage and achieve an average priority level of no more than 1.75. a. Define the decision variables. (3 Points) b. Develop the objective function. (3 Points) c. Write the constraints. (9 Points) d. Solve the problem in Excel. (10 Points: O.F. Section: 2 points, Constraints section: 3 points, Solver: 5 points)