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Unformatted text preview: This examination has 12 pages including this cover The University of British Columbia Final Examination – 11 Dec 2009 Mathematics 340 Linear Programming Closed book examination Time: 150 minutes Name Signature UBC Student Number Special Instructions: • Students are invited to write on both sides of each sheet. • To receive full credit, all answers must be supported with clear and correct derivations. • No calculators, notes, or other aids are allowed. Rules governing examinations 1. All candidates should be prepared to produce their library/AMS cards upon request . 2. Read and observe the following rules : No candidate shall be permitted to enter the examination room after the expiration of one half hour, or to leave during the first half hour of the examination. Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambiguities in examination questions. CAUTION - Candidates guilty of any of the following or similar practices shall be immediately dismissed from the examination and shall be liable to disciplinary action. (a) Making use of any books, papers or memoranda, other than those authorized by the examiners. (b) Speaking or communicating with other candidates. (c) Purposely exposing written papers to the view of other candidates. The plea of accident or forgetfulness shall not be received. 3. Smoking is not permitted during examinations . 1 12 2 12 3 12 4 12 5 6 6 15 7 16 8 15 Total 100 11 Dec 2009 MATH 340 UBC ID: Page 2 of 12 pages  1. Consider the following problem: maximize ζ =- 5 x 1 + 6 x 2- 4 x 3 subject to 2 x 1 + 3 x 2- x 3 ≤ - 2- x 1 + 2 x 2 + 2 x 3 ≤ 3 x 1 , x 2 , x 3 ≥ (a) Write the dual problem. (b) Show that the dual problem is unbounded, by presenting a sequence of feasible inputs for the dual problem whose objective values diverge to-∞ ....
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