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Linear Programming – Graphical Solution Method. Hillier – OR Tutorial. Graphical Solution – Wyndor Glass Problem. x 2. 6. 1. x 1. x 1. 4. 1. What is the feasible region? Is the feasible region convex?. Graphical Solution Method – cont.
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Linear Programming – Graphical Solution Method Hillier – OR Tutorial
Graphical Solution – Wyndor Glass Problem x2 6 1 x1 x1 4 1 What is the feasible region? Is the feasible region convex?
Graphical Solution Method – cont. • Minimization Problem – objective function moves in a direction that reduces the objective value.
Graphical Solution Method – cont. • Multiple Optimal Solutions - the objective function is parallel to a constraint as it leaves the feasible region. max 3x1 + 2x2 s.t. x1/40 + x2/60 < 1 x1/50 + x2/50 < 1 x1 ,x2> 0 x2 60 10 Can you have exactly two optimal solutions? x1 x1 50 10
Graphical Solution Method – cont. • Infeasible LP – the feasible region is empty x2 60 • max 3x1 + 2x2 • s.t. x1/40 + x2/60 < 1 • x1/50 + x2/50 < 1 • x1> 30 • x2> 20 • x1 , x2> 0 10 x1 x1 50 10
Graphical Solution Method – cont. • Unbounded LP – the feasible region is unbounded, goes to infinity x2 6 • max 2x1 - x2 • s.t. x1 - x2< 1 • 2x1 + x2> 6 • x1 , x2> 0 1 x1 x1 5 1
