Question 1 [13] The Department of Sport Development has been given a grant of R600 million...

 

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Question 1 [13] The Department of Sport Development has been given a grant of R600 million to expand its public sport facilities. The city council has requested the following four different types of facilities: gymnasiums, soccer fields, tennis courts and swimming pools. The total demand by various neighbourhoods has been estimated to be seven gyms, ten soccer fields, eight tennis courts and twelve swimming pools. Each facility costs a certain amount, requires a certain number of hectares and has an expected usage as shown in the following table: Cost Hectares Expected usage million required Facility people/week Gymnasium 80 4 1500 Soccer field 24 8 3000 Tennis court 15 3 Swimming pool 40 5 500 1000 The department has located 50 hectares of land for construction (although more land could be located if necessary). The council has established the following list of prioritised goals: The Department of Sport Development must spend the total grant (the amount not spent will be returned to the government). The facilities should be used by 20000 or more people weekly (in total). If more land is required, the additional amount should be limited to ten hectares. The Department of Sport Development would like to meet the city council's demands. How- ever, this priority should be weighted according to the number of people expected to use each facility. The Department of Sport Development wants to avoid having to acquire land beyond the 50 hectares presently available. Formulate this problem as a goal programming model. Question 1 [13] The Department of Sport Development has been given a grant of R600 million to expand its public sport facilities. The city council has requested the following four different types of facilities: gymnasiums, soccer fields, tennis courts and swimming pools. The total demand by various neighbourhoods has been estimated to be seven gyms, ten soccer fields, eight tennis courts and twelve swimming pools. Each facility costs a certain amount, requires a certain number of hectares and has an expected usage as shown in the following table: Cost Hectares Expected usage million required Facility people/week Gymnasium 80 4 1500 Soccer field 24 8 3000 Tennis court 15 3 Swimming pool 40 5 500 1000 The department has located 50 hectares of land for construction (although more land could be located if necessary). The council has established the following list of prioritised goals: The Department of Sport Development must spend the total grant (the amount not spent will be returned to the government). The facilities should be used by 20000 or more people weekly (in total). If more land is required, the additional amount should be limited to ten hectares. The Department of Sport Development would like to meet the city council's demands. How- ever, this priority should be weighted according to the number of people expected to use each facility. The Department of Sport Development wants to avoid having to acquire land beyond the 50 hectares presently available. Formulate this problem as a goal programming model.