Quality Management

Pages: 16 (5344 words) Published: October 30, 2014
Introduction to Optimization Linear Programming 1.If an LP model has more than one optimal solution it has an infinite number of alternate optimal solutions. In Figure 2.8, the two extreme points at (122, 78) and (174, 0) are alternate optimal solutions, but there are an infinite number of alternate optimal solutions along the edge connecting these extreme points. This is true of all LP models with alternate optimal solutions. 2.There is no guarantee that the optimal solution to an LP problem will occur at an integer-valued extreme point of the feasible region. (An exception to this general rule is discussed in Chapter 5 on networks). 3.We can graph an inequality as if they were an equality because the condition imposed by the equality corresponds to the boundary line (or most extreme case) of the inequality. 4.The objectives are equivalent. For any values of X1 and X2, the absolute value of the objectives are the same. Thus, maximizing the value of the first objective is equivalent to minimizing the value of the second objective. 5.a.linear b.nonlinear c.linear, can be re-written as 4 X1 - .3333 X2 75 d.linear, can be re-written as 2.1 X1 1.1 X2 - 3.9 X3 SYMBOL 163 f Symbol 0 e.nonlinear 6. 7. 8. 9. 10. 11. 12. 13.X1 of TV spots, X2 of magazine ads MAX15 X1 25 X2(profit) ST5 X1 2 X2 100 (ad budget) 5 X1 0 X2 SYMBOL 163 f Symbol 70 (TV limit) 0 X1 2 X2 SYMBOL 163 f Symbol 50 (magazine limit) X1, X2 SYMBOL 179 f Symbol 0 SHAPE MERGEFORMAT 14. X1 tons of ore purchased from mine 1, X2 tons of ore purchased from mine 2 MIN90 X1 120 X2(cost) ST0.2 X1 0.3 X2 8 (copper) 0.2 X1 0.25 X2 6 (zinc) 0.15 X1 0.1 X2 5 (magnesium) X1, X2 SYMBOL 179 f Symbol 0 15.X1 number of generators, X2 number of alternators MAX250 X1 150 X2 ST2 X1 3 X2 SYMBOL 163 f Symbol 260 1 X1 2 X2 SYMBOL 163 f Symbol 140 X1, X2 SYMBOL 179 f Symbol 0 16.X1 number of generators, X2 number of alternators MAX250 X1 150 X2 ST2 X1 3 X2 SYMBOL 163 f Symbol 260 1 X1 2 X2 SYMBOL 163 f Symbol 140 X1SYMBOL 179 f Symbol 20 X2 SYMBOL 179 f Symbol 20 d. No, the feasible region would not increase so the solution would not change -- youd just have extra (unused) wiring capacity. 17.X1 proportion of beef in the mix, X2 proportion of pork in the mix MIN.85 X1 .65 X2 ST1X1 1 X2 1 0.2 X1 0.3 X2 SYMBOL 163 f Symbol 0.25 X1, X2 SYMBOL 179 f Symbol 0 18.R number of Razors produced, Z number of Zoomers produced MAX70 R 40 Z STR Z SYMBOL 163 f Symbol 700 R Z SYMBOL 163 f Symbol 300 2 R 1 Z SYMBOL 163 f Symbol 900 3 R 4 Z SYMBOL 163 f Symbol 2400 R, Z SYMBOL 179 f Symbol 0 19. P number of Presidential desks produced, S number of Senator desks produced MAX 103.75 P 97.85 S ST30 P 24 S SYMBOL 163 f Symbol 15,000 1 P 1 S SYMBOL 163 f Symbol 600 5 P 3 S SYMBOL 163 f Symbol 3000 P, S SYMBOL 179 f Symbol 0 20.X1 acres planted in watermelons, X2 acres planted in cantaloupes MAX256 X1 284.5 X2 ST50 X1 75 X2 SYMBOL 163 f Symbol 6000 X1 X2 SYMBOL 163 f Symbol 100 X1, X2 SYMBOL 179 f Symbol 0 SHAPE MERGEFORMAT 21. D number of doors produced, W number of windows produced MAX500 D 400 W ST1 D 0.5 W SYMBOL 163 f Symbol 40 0.5 D 0.75 W SYMBOL 163 f Symbol 40 0.5 D 1 W SYMBOL 163 f Symbol 60 D, W SYMBOL 179 f Symbol 0 22.X1 number of desktop computers, X2 number of laptop computers MAX600 X1 900 X2 ST2 X1 3 X2 SYMBOL 163 f Symbol 300 X1 SYMBOL 163 f Symbol 80 X2 SYMBOL 163 f Symbol 75 X1, X2 SYMBOL 179 f Symbol 0 23. T number of TV ads to run, M number of magazine ads to run MIN500 T 750 P ST3T 1P SYMBOL 179 f Symbol 14 -1T 4P SYMBOL 179 f Symbol 4 0T 2P SYMBOL 179 f Symbol 3 T, P SYMBOL 179 f Symbol 0 Case 2-1 For The Lines They Are A-Changin Errata In the first printing, this case refers to file Fig. 2-8.xls but the actual...
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