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Unformatted text preview: Homework 5 Solution
Page 411-problem 28:
Define if professor is assigned to time slot , , Then the formulation is Page 411-problem 29:
I have explained the problem during the Friday's discussion section. . All decision variables are nonnegative and integer valued. Page 522-problem 6:
The BB tree is plotted below. Please judge the optimal solution by yourself. Page 522-problem 7:
The BB tree is plotted below. Please judge the optimal solution by yourself. Page 523-problem 8:
I have explained the problem during the Friday's discussion section. The proof is outlined below.
Proof: We assume
If exists. , done; If not, then we must have . Choose . We argue that is optimal to node 1. There are two steps to show this.
Step (1): Let be the set of constraints for node 0. We infer that
. We can show that
Step (2): Let be the objective function. Assume the problem is a maximization problem. Then
. We infer that node 1. satisfies node , and
satisfies must be an optimal solution to ...
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- Fall '07