IEOR 3608, Fall 2002: Homework 3

Assigned: Wednesday, September 25, 2002
Due: Wednesday, October 2, 2002, in 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.

Problems

  1. p. 140, Problem A1. Show your steps, do not just give the solution.
  2. p. 140, Problem B5.
  3. p. 148, Problem A1. Show the steps of the simplex algorithm, do not just give the solution.
  4. 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
  5. 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.
  6. Extra Credit: Explain why we don't include < or > constraints in a linear program.

Switch to:

cliff@ieor.columbia.edu