Department has received a federal grant of $6,000,000 to expand its public
recreation facilities. City Council representatives have demanded that four
types of facilities be considered for inclusion in the expenditures from the
grant: gymnasiums, athletic fields, tennis courts, and swimming pools. In fact,
the demand by various communities in the city, and supported by the City
Council, has been for 7 gymnasiums, 10 athletic fields, 8 tennis courts, and 12
swimming pools. Each facility costs a fixed amount, requires a fixed number of
acres, and is expected to be used a specified amount. A gymnasium costs
$800,000 to build, requires 4 acres of land, and is expected to be used by
1,500 people each week. An athletic field costs $240,000 to develop, requires 8
acres of land, and is expected to be used by 3,000 people each week. A tennis
court requires $150,000 to construct, requires 3 acres of land, and is expected
to be used by 500 people each week. Finally, a swimming pool costs $400,000 to
build, requires 5 acres of land, and is expected to be used by 1,000 people
each week. The Parks and Recreation Department has located a total of 50 acres
of land for construction of these various projects in appropriate locations.
Additional land could be acquired if necessary. The department has established
the following goals, listed in their order of priority:
The total grant should be spent since any unallocated funds
must be returned.
The facilities developed, in total, should be used by at
least 20,000 people each week.
The acquisition of additional acreage should be avoided.
The requests for new facilities should be weighted according
to the number of people expected to use each facility.
Q: Formulate a linear goal programming model that can be
used to determine the number of each type of facility to be constructed to best
achieve the goals of the Santa Ana City Parks and Recreation Department and
determine the optimal facility development plan using the Management Scientist
software, including the quantity of each facility type developed, and the
levels of goal achievement and if the goal achieved or is failure indicated
