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CO-351-1071-Final_exam

# CO-351-1071-Final_exam - CO 351 Network Flows Final Exam...

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CO 351 Network Flows, Final Exam, Winter 2007 Page 1 UNIVERSITY OF WATERLOO FINAL EXAMINATION WINTER TERM 2007 Surname: First Name: Id.#: Course Number CO 351 Course Title Network Flows Instructor J. K¨onemann Date of Exam April 18th, 2007 Time Period 9-11:30 a.m. Number of Exam Pages 14 (including this cover sheet) Exam Type Closed Book Additional Materials Allowed None Additional Instructions Write your answers in the space provided. Problem Value Mark Awarded Problem Value Mark Awarded 1 16 5 15 2 15 6 16 3 19 4 19 TOTAL 100

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CO 351 Network Flows, Final Exam, Winter 2007 Page 2 Problem 1: Maximum Flow – Modelling (16 Marks) The local express courier company KW-Express has 7 different types of packages to deliver. There are three packages of each type. The company has 5 trucks available for delivery and the numbers of packages that each truck can carry are as follows: Truck 1 2 3 4 5 Capacity (# packages) 6 4 5 4 3 Set up a maximum flow problem that can be used to determine whether the packages can be loaded onto the trucks such that no truck carries more than one package of the same type. Make sure to include a capacity c ( a ) for each arc a in your digraph. Describe how an s, t -flow in your digraph corresponds to a solution to the packing problem and vice versa.
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CO 351 Network Flows, Final Exam, Winter 2007 Page 4 Problem 2: Maximum Flow – Computing Flows (15 Marks) The following figure shows a digraph D on 6 nodes where s = 1 and t = 6 . Each arc uv in the figure is labeled with a tuple ( x uv , c ( uv )) , and each node v is labeled with its height h ( v ) .
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