.Fun City Texas is trying to determine the type and location of recreational fac

.Fun
City Texas is trying to determine the type and location of recreational
facilities to build during the next decade.
Four types of facilities are under consideration: golf courses swimming pools gymnasiums and
tennis courts. Six sites are under
consideration. If a golf course is
built it must be built at either site 1 or 6.
Other facilities can be built at sites 2-5. The amounts of available land (in thousands
of square feet) at sites 2-5 are given in Table 3.1. 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 3.2. The
number of user days (in thousands) for each type of facility (Table 3.3)
depends on where it is built. Table
3.1: Available Land by SiteSite2345Land708095120 Table
3.2: Cost and Land RequirementsConstruction CostMaintenance costLand RequiredGolf$340$80N/ASwimming$300$3629Gymnasium$840$5038Tennis Courts$85$1745 Table
3.3: User Days Site123456Golf3127Swimming25213232Gymnasium37292838Tennis Courts20232220The following priorities (in
order of importance) were established:
1. Construction costs
should not exceed $1.2 million.2. User days should exceed
2000003. Annual maintenance cost
should not exceed $200000.FORMULATE this goal programming
problem as a linear programming model. Formulate the goals as goal
constraints. Use preemptive penalties
and solve using the linear/integer algorithm.
Do not use goal programming algorithm.
In your formulation be sure to show all constraints (e.g. content goal
non-negative); show definitions of decision and deviation variables; show
objective function; assign values to the penalties on the deviation variables
and explain why you chose those values.
Delineate your solution. Remember
the value of the objective function does not have a physical meaning and
everyone may not have the same value for the objective function.