Homework 2

Due in class, 9 February, 2012
  1. (Cowen) Solve the following problem by the simplex method:
    Minimize -3x1 - 2x2 - 4x3 subject to
    x1 + x2 + 2x3 ≤ 4
    2x1 + 3x3 ≤ 5
    2x1 + x2 + 3x3 ≤ 7
    x1 , x2 , x3 ≥ 0
  2. The following linear program was discussed in class (and in HW1, Exercise 2): minimize -3x1 - 2x2 subject to x being nonnegative and
    -2x1 + x2 ≤ 1
    x1 ≤ 2
    x1 + x2 ≤ 3
    Convert it to standard form and answer the following questions for each vertex:
    Which other vertices (if any) could the simplex method go to from that vertex?
    Which other vertices could you go to in a single pivot?