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Unformatted text preview: (e) Suppose that the number of hours available in the dry room decreases by 30. Give a bound for the decrease in the total proﬁt. (f) If we replace the last constraint with P 1-P 2 ≥ 0, would the amount of P 1 produced in the optimal solution be positive? Problem 4.26 Let A be a given matrix. Show that exactly one of the following alternatives must hold. (a) There exists some x 6 = 0 such that Ax = 0, x ≥ 0. (b) There exists some p such that p t A > t . proof: Assume that both (a) and (b) hold. 2 Now ﬁnish the proof by showing that if (a) doesn’t hold, then (b) holds. Why is this enough? Problem 4.14 Give an example in which the primal problem has a degenerate optimal basic feasible solution, but the dual has a unique optimal solution. 3...
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- Spring '05
- Optimization, allowable decrease, P1 P2, Allowable Increase, optimal dual variables, Review Duality and Sensitivity