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Homework 5

# Homework 5 - And optimal primal solution = optimal dual...

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e62 Introduction to Optimization Spring 2008 Prof. Ben Van Roy May 2, 2008 Homework Assignment 5: Due May 16 PART A Do problems 4.6.2, 4.6.3, 4.6.4, 4.6.8, and 4.6.10 from the notes. PART B Problem 1. Provide numerical examples (object function and constraints) for each of the following cases. Say whether the primal and dual are unbounded and whether each has an optimal solution. a) Primal feasible, dual feasible. ( Example answer: Both primal and dual have optimal solutions.
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Unformatted text preview: And optimal primal solution = optimal dual solution ). b) Primal feasible, dual infeasible. c) Primal infeasible, dual feasible. d) Primal infeasible, dual infeasible. Problem 2. Write the dual of the following LP problem. min Σ n v =1 y v s.t. y v + y w ≥ 1 , ∀ v 6 = w,v,w ∈ { 1 , 2 ,...,n } y v ≥ , ∀ v ∈ { 1 , 2 ,...,n } Hint: try n=2,3,4 to ﬁnd the pattern...
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