Questions from Kupferschmid, Chapter 5 (available on LMS):

• 5.5.13(b) (lecture 11C). Hints: (i) express the unbd problem as an inequality constrained problem in the variables x₃ and x₄; (ii) you should only need one artificial variable in Phase I for the dual problem.
• 5.5.14(d), (e), (f) (lectures 11C, 11B) Hint: Construct the dual of the full 5-variable primal problem, so the dual has 5 constraints and 3 variables. This should make part (f) more straightforward, since the number of dual constraints is equal to the dimension of the ray.
• 5.5.21 (lecture 12C)
• 5.5.22 (lecture 12C)
• 5.5.28 (lecture 12A) Hint: You can work with the standard primal-dual pair, and use the relationships between the primal and dual optimal tableaus at the end of handout 12A.

In addition, read Sections 5.1 and 5.2 from the text.

Also, install AMPL on your computer and try solving a test problem, for example the problem in 5.5.25 (you don’t need to submit anything for this question).

Solving the homework problems (and other problems from the text) will improve your understanding of the material.

Working out the problems yourself will greatly improve your understanding of the material and help you on the exams.

You can ask questions on piazza, in addition to using office hours or email.