Quality Management
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 MAX 15 X1 25 X2 (profit) ST 5 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 MIN 90 X1 120 X2 (cost) ST 0.2 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 MAX 250 X1 150 X2 ST 2 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