Linear Prog COP4355_Part_15

Linear Prog COP4355_Part_15 - Chapter 5 Linear Programming...

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64 Chapter 5 Linear Programming: Computer Applications 5.2 Z = 51.44928 5.3 Z = 131.2329 5.4 Z = 91.8 5.5 Z = -1418481 (infeasible) 5.6 Z = 1725 5.7 Z = 3255.146 5.8 Z = 7872 5.9 Z = 112200 5.10 MAX Z: 4X 1 + 3X 2 + 6X 3 + X 4 + 4X 5 + 7X 6 + 3X 7 + 10X 8 + 5X 9 +3X 10 Subject to: X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X 8 + X 9 + X 10 = 1 X 1 .05 X 1 .1 X 2 .02 X 2 .2 X 3 .1 X 3 .2 X 4 .02 X 4 .1 X 5 .04 X 5 .25 X 6 .1 X 6 .3 X 7 .01 X 7 .05 X 8 .02 X 8 .05 X 9 .1 X 9 .5 X 10 .25 X 10 .5 Optimal Solution: X 1 = .05 X 8 = .05 S 15 = 0.08 Z MAX = 5.28 X 2 = .02 X 9 = .10 S 16 = 0.21 X 3 = .16 X 10 = .25 S 18 = 0.04 X 4 = .02 S 7 = 0.2 S 20 = 0.4 X 5 = .04 S 9 = 0.03 S 21 = 0.25 X 6 = .30 S 12 = 0.05 X 7 = .01 S 14 = 0.04 Interpretation: Variables X 1 through X 10 are the product proportions. The other variables in the solution are slack variables. All of the products except X 3 are at either the maximum or minimum boundaries so have either a single positive or negative slack representing the range between maximum and minimum boundaries. X 3 has a value between its 5.10 (continued) maximum and minimum boundaries and thus both a positive and a negative slack.
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