IEOR 3608, Fall 2001: Homework 09

General Instructions

1. This homework covers material from lectures on 11/14, 11/19 and 11/21.
2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
3. Numbered problems are all from the textbook Introduction to Mathematical Programming.

Problems

1. p. 411. Problem A6. Formulate this problem as a shortest path probelm.
2. p. 412. Problem A10.
3. p. 424. For the network in Figure 22:
   1. Find the maximum flow using the Ford-Fulkerson algorithm. At each step show the original graph and the residual graph.
   2. Find a minimum cut in the network.
   3. Write down a linear program for the maximum flow in this network. What are the values of the variables in an optimal solution to this linear program?
   4. Write down the dual of the linear program from the previous part. What are the values of the variables in an optimal solution to the dual lienar program.
4. p. 424. Problem B12.
5. p. 424. Problem B16.
6. p. 453. Problem A3.
7. p. 459. Problem B4.
8. Extra credit: p. 454. Problem B7. Formulate this LP and solve it any way you like.

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