M306_2H - 1 • Graphical Solution Method for Linear...

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Unformatted text preview: 1 • Graphical Solution Method for Linear Programming Model 2 • Announcements § Read Chapters 2 and 3 in book. § Class next Wednesday will be held in a computer lab. • Lab 1: • Room • Last Name • Room • Last Name • 9:00 • Lab 2 KRAN • A - M • ENAD 138 • N - Z • 10:3 • Lab 2 KRAN • A - J • ENAD 138 • K - Z • 1:30 • Lab 2 KRAN • A - H • SC 283 • I - Z 3 • Linear Programming Model of Catch-Big Problem Max 500,000x1 + 700,000x2 s.t. 20,000 x1 + 30,000 x2 < 190,000 x1 < 6 x1 + x2 < 8 x1, x2 > 4 • Feasible Solutions and Optimal Solution § Feasible solution : the values of decision variables that satisfy all the constraints § Feasible region : all the feasible solutions § Optimal solution : feasible solution with the largest (or smallest) objective function value for maximization (or minimization) § A graphical solution method can be used to solve a linear program with two variables. 5 1 2 3 4 5 6 § Values for decision variables points in a plane with axes: • Picture the Values For Decision Variables 5 4 3 2 1 x 2 x1 6 • Example 2: Graphical Solution Method § Given a linear programming model: Min 5 x 1 + 2 x 2 s.t. 4 x 1 - x 2 > 12 x 1 + x 2 > 4 x 1, x 2 > • 7 • Slide • • Summary: How to Graph a Constraint 1. Plot the line corresponding to the equality form of the constraint. (Pick two points on the line and join them) 2. Check which side of the line contains the feasible solutions. You can randomly pick a point, say the origin (0,0), and check if the point satisfies the inequality. If yes, the side which contains this point is the feasible solution side. If no, then the side which does not contain this point is the feasible solution side. 8 • Example 2: Graph Constraints § Graph the region of points satisfying 4x1 - x2 > 12 : 5 4 3 2 1 1 2 3 4 5 6 x 2 x1 9...
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This note was uploaded on 01/31/2011 for the course MGMT 306 taught by Professor Staff during the Fall '08 term at Purdue.

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M306_2H - 1 • Graphical Solution Method for Linear...

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