MA/IE/OR 505-001: Linear Programming
Homework 3
Instructor: Dr. Kartik Sivaramakrishnan
INSTRUCTIONS
Due in class on Thursday, March 22, 2007. No late homeworks will be accepted without
prior instructor approval. All problems are from Chv´atal unless otherwise specified. Please
read Chapters 7 and 10 in Chv´atal before beginning the assignment.
1. Problem 7.1, Page 116. Solve Problem 2.1(a) only! Do only the first two iterations by
hand. You can complete the rest of iterations using the revised simplex code that I
have posted on the course webpage.
2. Consider the following LP
max Z=−x1−x2
s.t. −2x1−x2≤4
−2x1+ 4x2≤ −8
−x1+ 3x2≤ −7
x1, x2≥0
(a) Solve the LP using the two phase simplex method.
(b) Solve the LP using the dual simplex method, i.e., by applying the simplex method
on dual dictionaries as discussed in class.
(c) Which method is more efficient with regard to the number of iterations? For the
two phase method, you should count the number of iterations in both phases of
the simplex method.
(d) Solve the LP using the revised dual simplex method (see Box 10.1 on page 155
of Chv´atal). Do only the first two iterations by hand. You can complete the rest
of the iterations using the dual simplex code that I have posted on the course
webpage. Verify that your results in the various iterations are identical to those
in part (b).
3. Problem 10.2, Page 167. In each case, use sensitivity analysis to reoptimize the new
LP.
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