A city parks department has £600 million to build recreational facilities and wants to determine how
many of each facility to build. The four types of facilities listed below are considered. The total
demand has been estimated to be 7 gyms, 10 athletic fields, 8 tennis courts and 12 swimming pools.
For each facility, the cost, number of hectares required and expected usage, are shown below.
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Athletic field
Tennis court
Swimming pool
Cost (Emillions)
Required Hectares
Expected Usage (people/week)
The parks department has a total of 50 hectares of land for construction (although more land could
be located if necessary). The council has established the goals listed below. The objective of the goal
programming model is to minimize the deviation from these goals.
1. The parks department should spend the total £600 million (otherwise the amount not spent will be
returned to the government).
2. The facilities should be used by 20,000 or more people weekly.
3. The parks department wants to avoid having to acquire land beyond the 50 hectares presently
available.
4. If more land is required, the additional amount should be limited to 10 hectares.
5. The parks department would like to meet the estimated demand for each type of facility.
Write down all the required algebraic expressions to express the goal programming model for the
above optimization problem. For each algebraic expression, make sure to explain parameters,
decision variables and the rationale for the formulation.
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