Math_340_December_2008

# Math_340_December_2008 - This examination has 13 pages...

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Unformatted text preview: This examination has 13 pages including this cover The University of British Columbia Final Examination – 11 Dec 2008 Mathematics 340 Linear Programming Closed book examination Time: 150 minutes Name Signature UBC Student Number Special Instructions: 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 16 4 4 5 8 6 16 7 12 8 12 9 8 Total 100 11 Dec 2008 MATH 340 UBC ID: Page 2 of 13 pages [12] 1. Study the following problem. maximize f = 5 x 1 + x 2- x 3 subject to 3 x 1 + x 2- x 3 ≤ - 2 3 x 1- x 2- 2 x 3 ≤ - 3 x 1 ≤ 2 x 1 , x 2 , x 3 ≥ (a) By comparing the objective function and the constraints, or otherwise, show that this problem cannot be unbounded. [2 marks] (b) Find a basic feasible solution. [5 marks] (c) Find all optimal solutions. [5 marks] Continued on page 3 11 Dec 2008...
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Math_340_December_2008 - This examination has 13 pages...

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