IEOR 3608, Fall 2002: Homework 01

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.

Problems

1. p. 52, Problem A4 (formulate the LP) and p.60, Problem A2 (graphically solve the LP).
2. p. 66, Problem A8. Show the graphical solution.
3. p. 69, Problem 3. For part a, in order to verify, you must formulate and solve the LP.
4. p. 76, Problem 4. Formulate the LP, but you do not have to solve.
5. 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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