The Santa Ana, California, City Parks and Recreation 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 acheived or is failure indicated