11 Gotham City is trying to determine the type and location of recreational facilities to be built during the next decade. Four types of facilities are under consideration: golf courses, swimming pools, gymnasiams, and tennis courts.

Six sites are under consideration. If a golf course is built, it must be built at either site 1 or site 6. Other facilities may be built at sites 2–5. The available land (in thousands of square feet) at each site is given in Table 64.

The cost of building each facility (in thousands of dollars), the annual maintenance cost (in thousands of dollars)

for each facility, and the land (in thousands of square feet)

required for each facility are given in Table 65.

The number of user days (in thousands) for each type of facility depends on where it is built. The dependence is given in Table 66.

a Consider the following set of priorities:

Priority 1 Limit land use at each site to the land available.

Priority 2 Construction costs should not exceed $1.2 million.

Priority 3 User days should exceed 200,000.

Priority 4 Annual maintenance costs should not exceed

$200,000.

For this set of priorities, use preemptive goal programming to determine the type and location of recreation facilities in Gotham City.

b Consider the following set of priorities:

Priority 1 Limit land use at each site to the land available.

Priority 2 User days should exceed 200,000.

Priority 3 Construction costs should not exceed $1.2 million.

Priority 4 Annual maintenance costs should not exceed

$200,000.

For this set of priorities, use preemptive goal programming to determine the type and location of recreation facilities in Gotham City.

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TABLE 64 Land Site 2 3 4 517 70 88 80 95 120 TABLE 65 Construction Maintenance Site Golf Cost Cost 340 80 Swimming 300 36 Gymnasium 840 50 Tennis courts 85 17 224 Land Required Not relevant 29 38 45