Assigned:
Sunday, September 24, 2001
Due:
Friday, September 28, 2001, 4PM, in boxes outside IEOR department office
General Instructions
- This homework covers material from lecture on 9/24.
- For each problem where you have to solve using the simplex method,
you should show your work. In particular, you should show the results
of each iteration, either as a tableau, or as a set of equations. You
can follow the details either of the method used in class, or the one
used in the textbook.
- 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.
- Numbered problems are all from the textbook Introduction to
Mathematical Programming.
Problems
- p. 140, Problem A1. Show your steps, do not just give the solution.
- p. 140, Problem B5.
- p. 148, Problem A1. Show the steps of the simplex algorithm, do
not just give the solution.
- 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
- Consider the following linear program:
minimize 2 x1 + x 2
subject to
x1 <= 5
x 1 + x2 >= -3
x2 >= 0
Convert this LP into standard form (as a maximization problem) and
solve it using simplex. Show your work.
Switch to:
cliff@ieor.columbia.edu