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as8 - CO 350 Assignment 8 – Winter 2009 Due Monday March...

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CO 350 Assignment 8 – Winter 2009 Due: Monday March 30 at 10 a.m. Solutions are due in drop box #2 , outside MC 4066 by the due time: Slot #9 (A-F), Slot #10 (G-L), Slot #11 (M-R), Slot #12 (S-Z). Write your name, ID# and Section# clearly. Marks will be deducted if any of this info is missing or incorrect. Section 1: J. Cheriyan, TTh 10-11:20 a.m. Section 2: E. Teske, MWF 10:30-11:20 a.m. Please acknowledge all outside sources, help and collaboration in your submission. Policy for marking complaints : If you have any complaints about the marking of assignments or the midterm exam, then you should first check your solutions against the posted solutions. After that, if you see any marking error, then you should return the assignment (or exam) to your instructor within one week and with written notes on all the marking errors; you may write the notes on the first/last page or else attach a separate sheet. ( ) Reading : Read Chapters 10 and 11, before attempting the exercises. 1. Consider the linear programming problem ( P ) max { c T x : Ax = b, x 0 } , where c T = bracketleftbig 0 , - 1 , 2 , 1 , 2 bracketrightbig , A = 2 - 1 5 - 4 - 1 - 1 1 1 - 1 0 1 2 - 1 1 1 , and b = 4 2 10 . Given B = { 3 , 4 , 5 } is a feasible basis. (Note: Parts (d) to (i) are independent of each other.) (a) Find the basic solution x * determined by basis B . (b) Find the solution y of A T B y = c B . (c) Compute ¯ c 1 and ¯ c 2 and show that x * is an optimal solution. (d) Suppose that c 1 in ( P ) is changed from zero to a real number θ . For what values of θ is x * still optimal?
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