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FFA 01 Integer Model Example
A community council must decide which recreation facilities to construct in its community. Four new recreation facilities have been proposed: a swimming pool, a tennis center, an athletic field, and a gymnasium. The council wants to construct facilities that will maximize the expected daily usage by the residents of the community subject to land and cost limitations. The expected daily usage and cost and land requirements for each facility follow.
Recreation FacilityExpected Usage
(people/day)
Cost ($)Land Requirements
(acres)Swimming pool
Tennis center
Athletic field
Gymnasium300
90
400
15035,000
10,000
25,000
90,0004
2
7
3
The community has a $120,000 construction budget and 12 acres of land. The swimming pool and tennis center must be built on the same part of the land parcel; therefore, only one of these two facilities can be constructed. The council wants to know which of the recreation facilities to construct in order to maximize the expected daily usage. The model for this problem is formulated as follows.
Zmax = 300x1 + 90x2 + 400x3 + 150x4
subject to:
$35,000x1 + 10,000x2 + 25,000x3 + 90,000x4 < $120,000
4x1 + 2x2 + 7x3 + 3x4 < 12 acres
x1 + x2 < 1 facility
x1, x2, x3, x4 = 0 or 1
where
x1 = construction of a swimming pool
x2 = construction of a tennis center
x3 = construction of an athletic field
x4 = construction of a gymnasium
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