Question NO. 3 (20 Marks) Formulate a Goal Programming model for the following city recreation authority, A city parks and recreation authority has been given a federal grant of $600,000 to expand its public recreation facilities. Four different types of facilities have been demanded by city council members speaking for their constituents: gymnasiums, athletic fields, tennis courts, and swimming pools. In fact the demand by various communities has been for seven gyms, ten athletic fields, eight tennis courts, and twelve swimming pools. However, each facility costs a certain amount, requires a certain number of acres, and has an expected usage. These parameters are sum- marized in the following table: Required Acres Facility Gymnasium Athletic Field Tennis Court Swimming Pool Cost ($) $80,000 24,000 15,000 40,000 4 8 3 5 Expected Usage (people/week) 1,500 3,000 500 1,000 The park authority has presently located fifty acres of land for construction (although more land could be located if necessary). The authority has established the following list of prioritized goals: P: The authority must spend the total grant or the amount not spent will be returned to the federal government Pz: The park authority desires the facilities be used by 20,000 people or more weekly Ps: The park authority wants to avoid securing extra land other than the fifty acres presently available. P. They would like to meet the demands of the city council members for the new facilities. However, this priority should be weighted according to number of people estimated to use each facility. Ps: If the authority must secure more land, they desire to limit it to ten acres