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AMS 341 (Fall, 2023)

Operations Research I: Deterministic Models

Homework Set # 6

Due on BrightSpace by noon (12 pm), Friday, October 27, 2023.

Read Chapter 6 Sections 5,6,7,8

Submit the following two problems:

(1). What is the dual of the following LP:

min z = X1 + 2Y 1 − Y 2

s.t. X1 + Y 2                       ≥ 2

      Y 1 + Y 2                      ≥ −3

      Y 1, Y 2                         ≥ 0

           X1                            unrestricted

(2). True or False? Give a brief explanation or counterexample:

(a). For a max problem in normal (symmetric) form all dual prices are non negative.

(b). An LP in normal (symmetric) form and its dual must have the same number of variables.

(c). If a primal LP is unbounded then its dual must be infeasible.

(d). If a primal LP is infeasible then its dual must be unbounded.