exam1soln

# exam1soln - 1 IE 220 Fall 2006 Professor Snyder October 5,...

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1 IE 220 Fall 2006 Professor Snyder October 5, 2006 Name: Mid-Term Exam 1 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. The exam contains a few Fail Safes . If you cannot solve a problem whose solution is required to complete the subsequent problems, you may opt instead to use the Fail Safe as the solution to the problem. The solutions speciﬁed by the Fail Safes are incorrect , but you may proceed as though they are correct. I will still give partial credit for the incorrect answer that you provided. If you need more space, use the back of the page or come see me and I 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!

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2 1. ( 50 points ) The diagram below is a map of Springﬁeld, with several landmarks marked, as well as their coordinates (in miles). In Springﬁeld, all roads run parallel to the 2 axes (there are no diagonal roads). Therefore, the distance from a point ( a 1 ,a 2 ) to a point ( b 1 ,b 2 ) is given by | a 1 - b 1 | + | a 2 - b 2 | . x 1 x 2 (0,0) Springfield Elementary (3,0) Moe’s Tavern (0,3) Power Plant (3,3) Homer Simpson’s House Krusty the Clown is planning to open a new Krusty Burger restaurant somewhere in Spring- ﬁeld, and he needs your help to decide where. His objective is to minimize the total distance that all of his customers must travel to get to the restaurant. Each of the locations plotted above has a certain number of customers, as follows: Location # of Customers Springﬁeld Elementary 50 Moe’s Tavern 40 Power Plant 70 Homer’s House 100 (Homer counts as 100 customers because he eats a lot of hamburgers.) In addition, Krusty has to obey the following constraints: The restaurant must be located within the square shown in the map. The deep-fat friers in the restaurant consume a lot of power. Therefore, the restaurant must be located within 2 miles of the Power Plant. Due to the industrial-strength sludge that sometimes leaks out of Krusty’s dumpsters, the restaurant must be located at least 2 miles from Springﬁeld Elementary. Let x 1 and x 2 be the decision variables, representing the coordinates of the new restaurant.
3 Two points of clariﬁcation to avoid confusion: Krusty’s objective is to minimize the sum of the distances to each location times the number of customers at that location. Distances (in both the objective function and constraints) are calculated as described

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## This homework help was uploaded on 04/07/2008 for the course IE 220 taught by Professor Storer during the Spring '07 term at Lehigh University .

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exam1soln - 1 IE 220 Fall 2006 Professor Snyder October 5,...

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