hw10 - can lead to the optimal integer solution x 1 2 x 2...

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Homework 10 Due April 21, 2009 Exercise 2, page 376, parts (a) and (d) convenience, use x 1 as the ﬁrst branching variable at the starting node. (a) Maximize z = 3 x 1 + 2 x 2 , subject to 2 x 1 + 5 x 2 9, 4 x 1 + 2 x 2 9, x 1 0, x 2 0 and both are integer valued. (b) Minimize z = 5 x 1 + 4 x 2 , subject to 3 x 1 + 2 x 2 5, 2 x 1 + 3 x 2 7, x 1 0, x 2 0 and both are integer valued. Exercise 3, page 377 Repeat the preceding problem assuming that x 1 is a continuous variable. Exercise 1, page 383 Consider the following problem (Example 9.2-2 in the book): maximize z = 7 x 1 + 10 x 2 subject to - x 1 + 3 x 2 6 7 x 1 + x 2 35 x 1 0 , x 2 0 and integer . Show graphically whether or not each of the following constraints can form a legiti- mate cut. (a) x 1 + 2 x 2 10. (b) 2 x 1 + x 2 10 . (c) 3 x 2 10 . (d) 3 x 1 + x 2 15. Exercise 2, page 384 For the preceding problem, show graphically how the following two (legitimate) cuts

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Unformatted text preview: can lead to the optimal integer solution: x 1 + 2 x 2 ≤ 10 cut I , 1 Figure 1: Network for exercise 3, page 405. 3 x 1 + x 2 ≤ 15 cut II . Exercise 5, page 384 Show that, even though the following problem has a feasible integer solution, the frac-tional cut would not yield a feasible solution unless all the fractions in the constraint were eliminated: maximize z = x 1 + 2 x 2 subject to x 1 + 1 2 x 2 ≤ 13 4 x 1 ≥ , x 2 ≥ 0 and integer . Exercise 3, page 405 For the network shown in Figure 1, it is desirable to ﬁnd the shortest route from 1 to 7. Deﬁne the stages and the states using backward dynamic programming recursion, and solve the problem. 2...
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hw10 - can lead to the optimal integer solution x 1 2 x 2...

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