# IEOR 3608, Fall 2003: Homework 02

Assigned: Wednesday, September 17, 2003
Due: Wednesday, September 24, 2003, at the beginning of class

## 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. 97 , Problem A2. Formulate but do not solve the LP.
2. p. 130, Problem A3.
3. p. 139, Problem A3. Give a table and a graph like the one done in class.
4. p. 149, Problem A3. Show your work. (each step of the simplex algorithm).
5. Run the simplex algorithm on the linear program given in class on Monday, but make x2, your first choice for the entering variable. That linear program was

maximize 3x1 + x2 + 2 x3
subject to
x1 + x2 + 3 x3 <= 30
2 x1 + 2 x2 + 5 x3 <= 24
4 x1 + x2 + 2 x3 <= 36
x1,x2,x3 >= 0
6. Extra Credit: Put the following problem into standard LP form. (Hint: you may need to introduce a dummy variable.)
7.  min | x - 1 | + y s.t. x + y <= 17 3x - 2y >= 5 x,y >= 0

### Switch to:

cliff@ieor.columbia.edu