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Unformatted text preview: MS&amp;E111 Homework # 3 Introduction to Optimization Due: May 26, 2006 Prof. Amin Saberi Homework 3 You can discuss the problems with your partner but you have to write your solutions indi- vidually. Please write the name of the person with whom you discussed the solutions. Problem 1. You are going to visit a national park, and have never been there before. You are using a map to try and make the distance traveled as short as possible. There are 5 intermediate towns, A, B, C, D, and E, you may go through on your way to the park, and the distances between the various locations are given below. Miles between Adjacent Towns Town A B C D E Destination Origin 40 60 50--- A 10- 70-- B 20 55 40- C- 50- D 10 60 E 80 In the table above, a dash means that there is no direct road between the two locations. a) Draw the graph corresponding to the above problem. b) Give a linear program which will find the shortest path from Origin to Destination. c) Solve the problem in Excel. d) Suppose the numbers in the table now represented the time taken (rather than the dis- tance). What would be the minimum time taken to travel from Origin to Destination? e) Suppose the number in the table now represented capacities for water pipes connecting the various locations (in units of gal/sec). What is the maximum amount of water that can be pumped from Origin to Destination? Problem 2. The coach of a swim team needs to assign swimmers to a 200-yard medley relay team to compete in a tournament. The problem facing him is that his best swimmers are good in more than one stroke, so it is not clear which swimmer to assign to which stroke. The 5 fastest swimmers and the best times (in seconds) they have achieved with each of the strokes (for 50 yards) are given below. 2 MS&amp;E 111: Introduction to Optimization - Spring 06 Stroke Carl Chris David Tony Ken Backstroke 37.7 32.9 33.8 37.0 35.4 Breaststroke 43.4 33.1 42.2 34.7 41.8 Butterfly 33.3 28.5 38.9 30.4 33.6 Freestyle 29.2 26.4 29.6 28.5 31.1 The problem is to try to minimize the sum of the best times for the people competing in the race. a) Draw a network that describes this problem. Note that one person will not be assigned....
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- Spring '06