Graphical Solution to a 2 Variable LP To find the optimal solution graph a line

Graphical solution to a 2 variable lp to find the

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8 Graphical Solution to a 2-Variable LP X1 X2 10 20 40 50 60 80 finishing constraint carpentry constraint demand constraint z = 60 z = 100 z = 180 Feasible Region G A B C D E F H To find the optimal solution, graph a line on which the points have the same z-value. In a max problem, such a line is called an isoprofit line while in a min problem, this is called the isocost line. The figure shows the isoprofit lines for z = 60, z = 100, and z = 180
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9 Graphical Solution to a 2-Variable LP The last isoprofit intersecting (touching) the feasible region indicates the optimal solution for the LP. X1 X2 10 20 40 50 60 80 finishing constraint carpentry constraint demand constraint z = 60 z = 100 z = 180 Feasible Region G A B C D E F H
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10 Graphical Solution to a 2-Variable LP The optimal solution must lie somewhere on the boundary of the feasible region. The LP must have an extreme point that is optimal, because for any line segment on the boundary of the feasible area, the largest z value on that line segment must be assumed to be at one endpoint of the line segment. X1 X2 10 20 40 50 60 80 finishing constraint carpentry constraint demand constraint z = 60 z = 100 z = 180 Feasible Region G A B C D E F H
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Summary of the Graphical Solution Procedure for Maximization Problems Prepare a graph of the feasible solutions for each of the constraints. Determine the feasible region that satisfies all the constraints simultaneously. Draw an objective function line. Move parallel objective function lines toward larger objective function values without entirely leaving the feasible region. Any feasible solution on the objective function line with the largest value is an optimal solution. 11
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  • Fall '15
  • KOYUNCU
  • Optimization, Constraint, feasible region, Candidate solution, Giapetto LP

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