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Unformatted text preview: CO 350 Final Exam, Fall 2009 Page 1 UNIVERSITY OF WATERLOO FINAL EXAMINATION FALL TERM 2009 Surname: First Name: Id.#: Course Number CO 350 Course Title Linear Optimization Instructor J. Cheriyan TuTh 10:00 LEC 001 W.H. Cunningham MWF 10:30 LEC 002 Date of Exam December 11, 2009 Time Period 9:0011:30 am Number of Exam Pages 13 (including this cover sheet) Exam Type Closed Book Additional Materials Allowed NONE (Calculators are NOT allowed.) Additional Instructions Checkmark the box next to your Section number. Write your answers in the space provided. If you need more space for your solution, then use the back of the previous page. You may use results from the course with out proof, provided you state those results in full. There is one exception: If the ques tion asks for a proof of a particular result, then you must give a proof. Question MaxMarks Mark Awarded Question MaxMarks Mark Awarded 1 7 6 6 2 12 7 6 3 10 8 14 4 12 9 12 5 14 10 7 Subtotal 55 Subtotal 45 TOTAL 100 CO 350 Final Exam, Fall 2009 Page 2 1. [7 marks = 5 + 2] (a) Formulate an auxiliary problem (Phase 1 problem) for finding a feasible solution of the [5] following LP problem ( P ). Clearly indicate the artificial variables, and the slack variables. ( P ) maximize x 1 + x 2 + x 3 subject to 2 x 1 x 2 + 4 x 3  1 x 2 5 x 3  2 x 1 3 x 3 = 3 x 1 , x 2 , x 3 (b) Write down an initial basis B and an initial basic feasible solution x * for the auxiliary [2] problem. Do not solve the auxiliary problem . CO 350 Final Exam, Fall 2009 Page 3 2. [12 marks] Consider the LP problem ( P ) max z = c T x subject to Ax = b, x , where A = 6 1 3 1 2 1 1 1 1 1 , b = 10 3 1 , and c T = [ 60 , 10 , 30 , 10 , 10] . B = { 1 , 2 , 3 } is a feasible basis, and it determines the basic solution x * = [1 , 1 , 1 , , 0] T . Apply one complete iteration of the revised simplex method. Use the smallest subscript rules to determine entering and leaving variables....
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