New Optimal solution

In linear programming, the shadow price of a constraint is the difference between the optimised value of the objective function and the value of the objective function evaluated when the right hand side of a constraint is increased by one unit.

When the slack or excess variable for a constraint is positive in a linear problem’s optimal solution, then the constraint will have a zero shadow price.

For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price)...

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Chapter 5, Problem 16RP

Chapter 6.1, Problem 2P

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A pig weighting 200 pounds gains 5 pounds per day and costs 45 cents aday to keep. The market price for pigs is 65 cents per pound, but is falling 1 cent perday.a/ When should the pig be sold? What is the optimal profit?b/ What are the sensitivities of the optimal time and optimal profit with respect to the45-cent upcost?c/ What are the sensitivities of the optimal time and optimal profit with respect to the1-cent market depreciation?

Consider the following LP and its optimal tableau: max z = 3x1 + 2x2s.t. 2x1 + 5x2 ≤ 8 3x1 + 7x2 ≤ 10 x1, x2 ≥ 0 a) Find the dual of this LP and its optimal solution. b) Find the range of values of b2 for which the current basis remains optimal. Also find the new optimal solution if b2 = 5.

Chapter 6 Solutions

Operations Research : Applications and Algorithms

Ch. 6.1 - Prob. 1P Ch. 6.1 - Prob. 2P Ch. 6.1 - Prob. 3P Ch. 6.1 - Prob. 4P Ch. 6.1 - Prob. 5P Ch. 6.2 - Prob. 1P Ch. 6.2 - Prob. 2P Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Prob. 3P

Ch. 6.3 - Prob. 4P Ch. 6.3 - Prob. 5P Ch. 6.3 - Prob. 6P Ch. 6.3 - Prob. 7P Ch. 6.3 - Prob. 8P Ch. 6.3 - Prob. 9P Ch. 6.4 - Prob. 1P Ch. 6.4 - Prob. 2P Ch. 6.4 - Prob. 3P Ch. 6.4 - Prob. 4P Ch. 6.4 - Prob. 5P Ch. 6.4 - Prob. 6P Ch. 6.4 - Prob. 7P Ch. 6.4 - Prob. 8P Ch. 6.4 - Prob. 9P Ch. 6.4 - Prob. 10P Ch. 6.4 - Prob. 11P Ch. 6.4 - Prob. 12P Ch. 6.4 - Prob. 13P Ch. 6.5 - Prob. 1P Ch. 6.5 - Find the duals of the following LPs: Ch. 6.5 - Prob. 3P Ch. 6.5 - Prob. 4P Ch. 6.5 - Prob. 5P Ch. 6.5 - Prob. 6P Ch. 6.6 - Prob. 1P Ch. 6.6 - Prob. 2P Ch. 6.7 - Prob. 1P Ch. 6.7 - Prob. 2P Ch. 6.7 - Prob. 3P Ch. 6.7 - Prob. 4P Ch. 6.7 - Prob. 5P Ch. 6.7 - Prob. 6P Ch. 6.7 - Prob. 7P Ch. 6.7 - Prob. 8P Ch. 6.7 - Prob. 9P Ch. 6.8 - Prob. 1P Ch. 6.8 - Prob. 2P Ch. 6.8 - Prob. 3P Ch. 6.8 - Prob. 4P Ch. 6.8 - Prob. 5P Ch. 6.8 - Prob. 6P Ch. 6.8 - Prob. 8P Ch. 6.8 - Prob. 9P Ch. 6.8 - Prob. 10P Ch. 6.8 - Prob. 11P Ch. 6.9 - Prob. 1P Ch. 6.9 - Prob. 2P Ch. 6.9 - Prob. 3P Ch. 6.10 - Prob. 1P Ch. 6.10 - Prob. 2P Ch. 6.10 - Prob. 3P Ch. 6.11 - Prob. 1P Ch. 6.11 - Prob. 3P Ch. 6.11 - Prob. 4P Ch. 6.12 - Prob. 5P Ch. 6.12 - Prob. 6P Ch. 6.12 - Prob. 7P Ch. 6 - Prob. 1RP Ch. 6 - Prob. 2RP Ch. 6 - Prob. 3RP Ch. 6 - Prob. 4RP Ch. 6 - Prob. 5RP Ch. 6 - Prob. 6RP Ch. 6 - Prob. 7RP Ch. 6 - Prob. 8RP Ch. 6 - Prob. 9RP Ch. 6 - Prob. 10RP Ch. 6 - Prob. 11RP Ch. 6 - Prob. 13RP Ch. 6 - Prob. 14RP Ch. 6 - Prob. 15RP Ch. 6 - Prob. 17RP Ch. 6 - Prob. 18RP Ch. 6 - Prob. 19RP Ch. 6 - Prob. 20RP Ch. 6 - Prob. 21RP Ch. 6 - Prob. 22RP Ch. 6 - Prob. 25RP Ch. 6 - Prob. 29RP Ch. 6 - Prob. 33RP Ch. 6 - Prob. 34RP Ch. 6 - Prob. 35RP Ch. 6 - Prob. 36RP Ch. 6 - Prob. 37RP

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