# M306_2 - Graphical Solution Method for Linear Programming...

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1 Graphical Solution Method for  Linear Programming Model

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2 Announcements § Read Chapters 2 and 3 in book. § Class next Monday in computer labs.   9am A – K, go to Krannert Lab 2 9am L – Z, go to ENAD 135 10:30am A – J, go to Krannert Lab 2 10:30am K – Z, go to ENAD 135 1:30pm, Krannert Labs 1 and 2 3:00pm, Krannert Labs 1 and 2
3 It’s Tough Out There Ahajokes.com

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4 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 > 0
5 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.

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6 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
7 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 > 0

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8 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.
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## This note was uploaded on 01/17/2012 for the course MGMT 306 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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M306_2 - Graphical Solution Method for Linear Programming...

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