Ch7Solutions

# Ch7Solutions - C H A P T E R Linear Programming Models...

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85 T EACHING S UGGESTIONS Teaching Suggestion 7.1: Draw Constraints for a Graphical LP Solution. Explain constraints of the three types ( # , 5 , \$ ) carefully the first time you present an example. Show how to find the X 1 , X 2 inter- cepts so a straight line can be drawn. Then provide some practice in determining which way the constraints point. This can be done by picking a few X 1 , X 2 coordinates at random and indicating which direction fulfills the constraints. Teaching Suggestion 7.2: Feasible Region Is a Convex Polygon. Explain Dantzing’s discovery that all feasible regions are convex (bulge outward) polygons (many-sided figures) and that the opti- mal solution must lie at one of the corner points. Draw both con- vex and concave figures to show the difference. Teaching Suggestion 7.3: Using the Iso-Profit Line Method. This method can be much more confusing than the corner point ap- proach, but it is faster once students feel comfortable drawing the profit line. Start your first line at a profit figure you know is lower than optimal. Then draw a series of parallel lines, or run a ruler paral- lel, until the furthest corner point is reached. See Figures 7.6 and 7.7. Teaching Suggestion 7.4: QA in Action Boxes in the LP Chapters. There are a wealth of motivating tales of real-world LP applica- tions in Chapters 7–9. The airline industry in particular is a major LP user. Teaching Suggestion 7.5: Feasible Region for the Minimization Problem. Students often question the open area to the right of the constraints in a minimization problem such as that in Figure 7.10. You need to explain that the area is not unbounded to the right in a mini- mization problem as it is in a maximization problem. Teaching Suggestion 7.6: Infeasibility. This problem is especially common in large LP formulations since many people will be providing input constraints to the problem. This is a real-world problem that should be expected. Teaching Suggestion 7.7: Alternative Optimal Solutions. This issue is an important one that can be explained in a positive way. Managers appreciate having choices of decisions that can be made with no penalty. Students can be made aware that alternative optimal solutions will arise again in the transportation model, as- signment model, integer programming, and the chapter on net- work models. Teaching Suggestion 7.8: Importance of Sensitivity Analysis. Sensitivity analysis should be stressed as one of the most important LP issues. (Actually, the issue should arise for discussion with every model). Here, the issue is the source of data. When accountants tell you a profit contribution is \$8.50 per unit, is that figure accurate within 10% or within 10¢? The solution to an LP problem can change dramatically if the input parameters are not exact. Mention that sensitivity analysis also has other names, such as right-hand- side ranging, post-optimality analysis, and parametric programming.

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## This note was uploaded on 07/19/2009 for the course DSCI 3031 taught by Professor Smith during the Spring '09 term at University of Houston.

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Ch7Solutions - C H A P T E R Linear Programming Models...

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