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CASE ANALYSIS: CAVITE PARKS AND RECREATION DEPARTMENT The manager of Cavite Parks and Recreation Department for the town of Cavite is considering plans for her town's new park and recreation center. Her recommendations will be presented to the seven members of the Park and Recreation Commission at its regular monthly meeting to be held next week. A series of community meetings has been held to obtain public input. The information from the public has been used to help planners identify what types of facilities the public wants and estimate how much each facility might be used. Table 1 shows the information the planners have assembled on facility construction cost, annual operating expense, space requirements, and expected daily usage. There will be at most one baseball field, either lighted or unlighted. At least two lighted tennis courts must be built. Any additional tennis courts after the two can be either lighted or unlighted. The total number of tennis courts cannot be more than four. There will be at most one swimming pool (either indoor or outdoor). A separate gymnasium, a separate fitness center, or a single building housing the two might be built; however, separate buildings for both a gymnasium and fitness center would not be built. There must be at least one picnic area, either large or small and no more than two picnic areas. If two picnic areas are provided, one must be small and the other must be large. The total amount of space available for the facilities is 140,000 square feet. The voters have approved a bond issue for PhP2.5 million to pay for the initial costs of constructing the facilities. The park's operating budget is PhP360.000 per year.

Facity Baseball field (nightech Basebab field (lighted Tennis Court (unlighted Tennis Court (ted) Swimming pool outdoor) Swimming pool (indoor) Gymnasium Fitness Center Combined Gymnasium and Finess Center Picnic area arge) Picnic Area (sm Intial Cost, PhP Annual Operating Expense, PP Required Space, Square feet Average Anticipated Usage, Residents/ day 155,000 55,000 40,000 750 380,000 110,000 41.000 1100 90.000 25,000 15,000 120 150,000 55,000 16,000 180 425.000 140,000 21.000 1150 1,250,000 190,000 25,000 1300 500,000 65,000 20,000 250 350,000 50,000 12,000 325 700,000 80,000 25,000 400 50.000 30.000 44,000 500 30,000 20,000 22.000 250 1. Formulate the Integer Programming Model to maximize resident usage. 2. Solve the IP using Branch and bound Methods (show all the solution of subproblems using SOLVER) 3. What facilities should be built to maximize resident usage? (Solve the IP using SOLVER by making all decision variables integer) 4. How much will it cost to construct and operate the facilities identified in part (c)? 5. What will be the total average number of residents expected to use the facility each day? 6. How much space will be left without a designated use if those identified in part (c) are provided? 7. What factor(s) limit resident usage? Which ones are in excess? Facity Baseball field (nightech Basebab field (lighted Tennis Court (unlighted Tennis Court (ted) Swimming pool outdoor) Swimming pool (indoor) Gymnasium Fitness Center Combined Gymnasium and Finess Center Picnic area arge) Picnic Area (sm Intial Cost, PhP Annual Operating Expense, PP Required Space, Square feet Average Anticipated Usage, Residents/ day 155,000 55,000 40,000 750 380,000 110,000 41.000 1100 90.000 25,000 15,000 120 150,000 55,000 16,000 180 425.000 140,000 21.000 1150 1,250,000 190,000 25,000 1300 500,000 65,000 20,000 250 350,000 50,000 12,000 325 700,000 80,000 25,000 400 50.000 30.000 44,000 500 30,000 20,000 22.000 250 1. Formulate the Integer Programming Model to maximize resident usage. 2. Solve the IP using Branch and bound Methods (show all the solution of subproblems using SOLVER) 3. What facilities should be built to maximize resident usage? (Solve the IP using SOLVER by making all decision variables integer) 4. How much will it cost to construct and operate the facilities identified in part (c)? 5. What will be the total average number of residents expected to use the facility each day? 6. How much space will be left without a designated use if those identified in part (c) are provided? 7. What factor(s) limit resident usage? Which ones are in excess