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Unformatted text preview: CO 227  Homework assignment 1 Fall 10 Page 1 CO 227  Fall 10 Homework assignment #1: (Due at the beginning of the class, 10:30AM, on Monday, Oct 4th) Instructions: Please show all your work and justify your answers. Answers without proper justification will not be considered. Please list who you collaborated with. Clearly define what are your decision variables and write down your final model. Total value = 100 points Question 1 Shark feeding problem (20 points) The shark tank at Captain Nemos aquarium contains a number NS of sharks. Every day, each shark requires at least enough, but not too much, of each of NN nutrients. Let l ij denote the daily minimum requirement of nutrient i (in pounds) for shark j , and let u ij denote the maximum amount of nutrient i (in pounds) that shark j can ingest per day (for all i = 1 , . . . , NN , j = 1 , . . ., NS ). The sharks are fed a total number of NF different foods. Let n ik denote the amount of nutrient i (in pounds) in each pound of food k given to the sharks, and let c k be the perpound cost of food k (for all i = 1 , . . ., NN , k = 1 , . . ., NF ). All sharks are handfed, so that each shark will get exactly the food that it is supposed to. Moreover, there is a huge supply of food, so we can assume there is no limit on the maximum amount of food that can be used to feed the sharks....
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 Spring '10
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