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Discover how to solve optimization problems through graphical methods with step-by-step tutorials. Learn about feasible regions, convexity, minimization problems, multiple optimal solutions, and distinguishing between infeasible and unbounded situations. Dive into the Wyndor Glass Problem and maximize your knowledge in Linear Programming.
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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
