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Unformatted text preview: ENGR62/MS&E111 Fall 2005 Introduction to Optimization December 8, 2005 Prof. Ben Van Roy Final Exam Instructions This is a take-home, open book/notes exam. There are 3 questions. Each has equal weight. Partial credit is possible for each question provided that what you hand in is relevant and partially solves a problem. The exam is due at Packard 274 by 11:00PM (Vivek will make sure youre able to get in). Vivek will be there between 10-11PM to collect your exams. Collaboration is not permitted on this exam. Exam-related questions will not be answered by the teaching staff (unless you think there is a serious exam typo). If you are unsure about something in a question, do your best to answer it with the information given. Questions 1,2, and 3 require the use of Excel. Please print out and hand in with your exam the worksheets you use to solve the problems (no solution reports are necessary). PLEASE PRINT OUT AND ATTACH THIS COVER SHEET TO THE FRONT OF YOUR EXAM WITH YOUR NAME AND SIGNATURE. GOOD LUCK! Honor Code In recognition of and in the spirit of the Honor Code, I certify that I will neither give nor receive unpermitted aid on this examination and that I will report, to the best of my ability, all Honor Code violations observed by me. Name: Signature: 1: E62 Aid Suppose you are in charge of coordinating an aid campaign consisting in bringing medicaments from different cities of America and Europe to certain cities in Africa. The logistics group of the project determined that the best way to do it is in two phases. First bring the medicaments from the American and European origin cities to some selected big cities in Africa where the aid would be organized to be sent to the destination cities. Assume that there is only one type of medicament. The American or European city i ( i = 1 , ..., I ) has an availability of medicaments equal to S i . Our warehouse at transfer city j ( j = 1 , ..., J ) has a capacity T j ; that is, no more than T j units of medicaments can go into city j . Everything that goes into the transfer city j must go out to some destination city. The African destination city k ( k = 1 , ..., K ) has a demand D k of medicaments, which must be satisfied. The unit transportation cost from city i to the transfer city j is c ij , for i = 1 , ..., I and j = 1 , ..., J . The unit transportation cost from the transfer city j to the destination city k is d jk , for j = 1 , ..., J and k = 1 , ..., K . (a) (15 points) Formulate a linear program that minimizes the total transportation costs while satisfying the demand requirements of each city, without violating the availability and capacity constraints. (b) (12 points)Suppose the origin cities are San Francisco with an availability of 1,000 (units are in thousands of medicaments) and London with an availability of 1,000. There are two transfer cities: Addis Ababa in Ethiopia with a capacity of 800 and Nairobi in Kenya with a capacity of 1,500. The destination cities are: Adwa and Dese in Ethiopia with awith a capacity of 1,500....
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