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Unformatted text preview: ORIE 3300/5300 PRACTICE FINAL Fall 2008 (The original exam had more space for solutions.) 2.5 hours 1. Consider the system of constraints ( S ) x 1- x 3 + x 4 = 2- x 1 + x 2 + 2 x 3 + x 4 = 2 x 1 , x 2 , x 3 , x 4 ≥ . (a) [3 marks] Use Phase 1 of the simplex method to find a basic feasible solution. For each question below about the system ( S ), you do not need to explain your method of finding an answer. For example, you might just observe it, by inspection. However you must justify why your answer is correct. (b) [2 marks] Find a degenerate basic feasible solution. (c) [2 marks] Find a feasible solution that is not basic. (d) [1 mark] Find a basic solution that is not feasible. 1 2. An oil company runs several wells, stores, and refineries, listed in AMPL data files in sets well , store , and refinery . During one year, the company can pump no more than maxpump[w] barrels of oil at each well w , and must choose how to divide up all the oil it pumps there into amounts ship1[w,s] to ship to each store s , at a cost cost1[w,s] dollars per gallon. The company must also choose how to divide up the total amount of oil received at each store...
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- Fall '08