OR 641/MATH 689 - Linear Programming, Fall 2005

Homeworks to date

• Homework 1, assigned August 31, due September 9 :
  • Solve the following system  (a) via Gauss Jordan elimination  (b) via Gaussian elimination
          x₁   -  4x₂   - 2x₃  +    x₄  =  2
          x₁                         + 2x₄  =  3
          x₁   + 4x₂    +  x₃  + 2x₄  =  1
        2x₁   +  8x₂   + 4x₃  + 5x₄  = 7
• Homework 2, assigned September 4 due September 14 :
  • Page 19 problem 1
  • Page 24, problems 1, 2, 3. In problem 2, a drawing is not sufficient proof.
  • Page 29, problem 3
  • Page 52, problems 1, 2
• Homework 3, assigned September 14 due September 21:
  • Page 52 problems 3, 5
  • Page 55, problem 1(c).
  • Page 62, problems 1, 3
  • Page 69, problems 1(c, d,e)
• Homework 4, assigned September 21 due September 28:
  • Page 83 problems 1,3,4, 6
  • Page 92 problems 4, 5
• Homework 5, assigned September 28 due October 5
  • Page 105 problems 2(a),(b), 3. Use the formulas of Section 5.2.1.
  • Page 105 problem 5
  • Repeat Page 105 problems 2(a),(b) using the simplex tableau.
  • Page 116 problem 5
• Homework 6, assigned October 5 due October 12
  • Solve the problems of Page 105 problem 2(a),(b) using the revised simplex tableau
  • Page 116, problems 3, 4
  • Page 120 problems 1, 4
• Homework 7, assigned October 12 due October 19
  • Page 131, problem 1, 2(a), 4, 6, 10 (note that in problem 10, part (a) the last surplus variable should be s_m rather than s_n).
  • Page 142, problem 1
• Homework 8, assigned October 19 due October 26
  • Page 149 problems 3,5,
  • Page 157 problems 1, 2, 8, 12
• Homework 9, assigned November 9 due November 30
  • Page 163, problems 1, 3
  • Perform 3 iterations of the primal/dual algorithm for the problem
    Minimize -2x1-x2
    Subject to x1<=2
                   x1+x2<=4
                  x1, x2>=0.
    Start from the point x=(1,1)' and y=(-2,-2)'. You will need to put the problem in standard form.
  • Page 291 Problem 4
  • Read Section 7.6 excluding 7.6.1
• Homework 10, assigned November 30. will not be collected but it is strongly recommended that you do them for December 7.
  • Page 190, problems 2, 4
  • Page 198 problems 1(a), 2,5