IEOR 3608, Fall 2004: Homework 2

Assigned: Wednesday, September 22, 2004
Due: Wednesday, September 29, 2004, 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. 92, Problem A2. Formulate but do not solve the LP.
  2. p. 93, Problem A9. Formulate but do not solve the LP.
  3. p. 139, Problem A3. Give a table and a graph like the one done in class.
  4. Lenny Arprogram proposes the following method for solving a linear program that has n variables and n constraints. First, express the linear program as a system
    A x <= b,
    where A is an n by n matrix and x and b are n dimensional vectors. Next, left multiply both sides of the equation by A-1 (you can assume that A-1 exists) , giving
    A-1 A x <= A-1 b
    which is the same as
    x <= A-1 b .
    Now A-1 b is just a vector of numbers, so we can read off the solution. Is Lenny correct? Either prove that Lenny is correct, or give a counterexample.
  5. p. 149, problem A2.
  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

     


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cliff@ieor.columbia.edu