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Unformatted text preview: 1 IE 220 Fall 2007 Professor Snyder November 6, 2007 Name: MidTerm Exam 2 INSTRUCTIONS: Write neatly and show your work for each question. I will give partial credit for partial answers. You may not use your notes, slides, or textbook. You may use a calculator. If you need more space, use the back of the page, or see the proctor and he will give you more paper. You may remove the staple if you wish. Please put the pages back in the correct order at the end of the exam. There are 100 total points. Good luck! 2 1. ( 8 points ) In class we argued that the following claim is false : If an IP is infeasible, then its LP relaxation is also infeasible. (a) ( 5 points ) Give an example of a binary IP with two variables and at most two functional constraints that is infeasible but whose LP relaxation is feasible. (b) ( 3 points ) Sketch the feasible region of the LP relaxation of the IP you wrote in part (a), and draw the integer points on your sketch. 3 2. ( 12 points ) Mr. Burns would like to visit the fishtaco companies he has invested in. In the map below, each node is an intersection and each link is a street. The numbers on the links indicate the time it takes to walk from one endpoint to another. Mr. Burns has just eaten at Krustys Fish Tacos (marked KFT on the map) and now wants to go to Duff Taco (marked DT on the map) using the shortest possible route. DT E C D B A KFT 5 8 5 10 6 1 8 5 7 3 5 10 Solve this problem using the shortest path algorithm we discussed in class. Show your work in the table below and report the optimal solution and its total length. (Hint: It should take you no more than 5 iterations.) Connected Closest n th Solved Connected Total Nearest Minimum Last n Nodes Unsolved Distance Node Distance Connected 1 KFT Optimal path: Its length: 4 3. ( 29 points ) The Springfield KwikEMart needs your help to decide how much shelf space to allo cate to four different candy and gum products on its display rack near the cash register....
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 Spring '07
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