By D. Cox, E. Snell

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**Example text**

Complete familiarity with computer manuals is more important than knowing two or more methods of solving a simple example by hand. A second choice that the author has made was to eliminate all mathematical proofs from the chapter. On the one hand, some students who approach linear programming from a mathematics background find theorems, corollaries, and lemmas and their proofs to be necessary to their complete comprehension of the process. On the other hand, the vast majority of students whom I have taught linear programming find mathematical proofs to be extraordinary consumers of study time.

Each time you develop a new Zj — Cj row you are determining the relationship between the value of the problem a n d the right-hand-side values. Summarizing, the dual activity tells us the rate of change in the objective function per unit change in the availability of resources. Another useful piece of information is the penalty associated with not following the mix recommended by the optimal solution. Using the same sample problem, let us review this information. Maximize : Z = 2Xl + X2 + 0X3 + 0X4 + 0X5 (1) subject to Xx + 2X2 + X3 2XX + 3X2 + XA =10 (2) =12 (3) + X5 = 18 3*!

EXERCISES / 53 EXERCISES Perform feasible calculations on the following : A = 2 1 3 1 -1 2 -2 -4 6 Γ Γ 5 2 3 3 1 0 B C = -1 2 -2 [l 0 2 F = 0 1 2 4 -1 [5 3 -3 E = 1 (PI) D + E (P3) E - B + D (P5) AE (P7) a ß (P9) D " 1 (P2) (P4) (P6) (P8) (P10) [ 4. ) A>Fa-F Solve the following problems. These same problems should be used at the end of Chapter 3 (for the dual) and for Chapter 4 to test your knowledge of the algorithm. 4) 2Xl +2X2- X3<9 The problem requires one artificial variable. 3). 6. On computer printout, look for symbol A.