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assignment7_ProblemSet

# assignment7_ProblemSet - ORIE 3300/5300 Individual work...

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ORIE 3300/5300 ASSIGNMENT 7 Fall 2008 Individual work. Due: 3 pm, Friday October 31. 1. Read Section 4.2 (on a multiperiod production model) in the AMPL book. Read through the problem described in question 4-5. Do parts (a) and (b), and save your work (perhaps by putting it in an email to yourself): you will use it in a future recitation. 2. Consider the linear program maximize c T x subject to Ax = b x 0 , where c = 2 5 9 0 1 A = 0 1 1 1 - 1 1 1 2 0 1 b = 4 5 . (a) Is B = [3 , 2] a basis? (b) Write down the matrices A B and A N , and the vectors c B and c N . (c) Calculate A - 1 B . (d) Solve the equations A B u = b for u and A T B y = c B for y . (e) Use your answers to write down the tableau corresponding to B . (f) What is an optimal solution to the problem? 3. Consider again the problem in Q2. Suppose the current basis is B = [4 , 5]. Calculate the current values of the basic variables, ˆ x B . Perform one iteration of the revised simplex method from this basic feasible so- lution, using the least index rule for the entering and leaving variables. OVER 1

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4. Suppose you are given a linear program with variables x 1 , x 2 , . . . , x
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