IEOR 3608, Fall 2005: Homework 1

General Instructions

1. Please review the course information.
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, 4th Edition.

Problems

1. p. 55, Problem A1 and A2. Formulate the LP. Do not solve. Answer A2. Then, comment on whether each of proportionality, divisibility, additivity and certainty hold.
2. p. 68, Problems A1,2,3,4. Show your work.
3. p. 68, Problem A9. Show the graphical solution.
4. p. 71, Problem A4. Formulate the LP, and show the graphical solution.
5. p. 76, Problem B5. Formulate, but do not solve the LP.
6. Extra Credit:
   1. Is it always true for a 2 variable LP, that if it has multiple optimal solutions, then the objective function must be parallel to one of the constraints? Prove it, or find a counterexample.
   2. Is it always true for a 3 variable LP, that if it has multiple optimal solutions, then the objective function must be parallel to one of the constraints ? Prove it, or find a counterexample.

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