Form constraints and objective; Graph feasible region and find vertices; Optimise objective and interpret units; Unused resources/wastage; Integer-feasible solutions and parameter sensitivity
Example 1
Maximise P=6x+5y over vertices (0,0),(4,0),(0,3). Find the maximum value.
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Answer: 24
- Evaluate the objective at each feasible-region vertex. A linear objective reaches a maximum at at least one vertex of this bounded polygon.
Example 2
For x≥0,y≥0,x+y≤5, which point is feasible?
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Answer: (2,2)
- Both coordinates must be nonnegative and their sum no more than 5.
Example 3
Maximise x+y for nonnegative integers x,y satisfying 2x+2y≤5. Find the maximum integer value.
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Answer: 2
- The continuous bound is x+y≤2.5; integrality reduces the largest possible total to 2.