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Practice Prelim 1 Summer 2004

Practice Prelim 1 Summer 2004 - ORIE 320/520 Optimization I...

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ORIE 320/520 Optimization I Summer 2004 Prelim 1 Name: You have 2 hours and 30 minutes to answer all the questions in the exam. The total number of points is 110, and your grade will be the minimum among 100 and the number of points you receive. For questions with multiple parts, the point value of each part is given at the start of that part. Be sure to give full explanations for all of your answers and to show all your calculations. In most cases, the correct reasoning alone is worth more credit than the correct answer by itself. Your explanation need not be wordy, but it should be sufficient to justify your answer. You receive much more credit for an incorrect answer if you recognize that something that you have computed is not correct than if you merely pretend that it is correct. The exam is closed notes. You are allowed to use a calculator and a 2-sided 6 00 X 4 00 card (indexed card) with personal summary, prepared by your own hand writing (no photo copies are allowed). Read everything carefully, make sure you don’t overlook anything. Not all the parts are in the same level of difficulty! Please make sure that you do not spend too much time on one part. Good Luck! 1
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1. (13 + 7 + 5) Following there are AMPL model and data files as well as the results of the AMPL run. This is the model that you have solved in problem sets 1 and 2. In par- ticular, the model deals with allocation of oil from a set of suppliers to a set of locations: Model File: set SUPPLIERS; set LOCS; param u-limit { SUPPLIERS } ; param l-limit { LOCS } ; param cost { LOCS, SUPPLIERS } ; var Ship { LOCS, SUPPLIERS } > = 0 ; minimize Total-Cost: sum { s in SUPPLIERS, l in LOCS } 1000 * Ship[l,s] * cost[l,s]; subject to Supply-Constraints { s in SUPPLIERS } : sum { l in LOCS } Ship[l,s] < = u-limit[s]; subject to Demand-Constraints { l in LOCS } : sum { s in SUPPLIERS } Ship[l,s] > = l-limit[l]; Data File: set SUPPLIERS := A B C; set LOCS := L1 L2 L3 L4; param u-limit := A 450 B 350 C 500; param l-limit := L1 90 2
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L2 150 L3 250 L4 420; param cost : A B C := L1 10 12 9 L2 11 12 15 L3 10 9 12 L4 11 13 9; Results: 12 variables, all linear 7 constraints, all linear; 24 nonzeros 1 linear objective; 12 nonze- ros. MINOS 5.5: optimal solution found. 10 iterations, objective 8500000 Ship := L1 A 10 L1 B 0 L1 C 80 L2 A 150 L2 B 0 L2 C 0 L3 A 0 L3 B 250 L3 C 0 L4 A 0 L4 B 0 L4 C 420 ; (a) (13) Write down the specific LP that the above files aim to solve (i.e., the constraints and objective function using the
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