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Unformatted text preview: ISYE3133C - Engineering optimization Modeling Handout #3 A quantity y is known to depend upon another quantity x . A set of corresponding values has been collected for x and y and is presented in the following table. i 1 2 3 4 x i . . 5 1 . 1 . 5 y i 1 . . 9 . 7 1 . 5 We want to approximate the relation between x and y by fitting the best straight line y = mx + c through the points ( x i , y i ) in the table. To achieve this we need to find parameters m and c . For a particular choice of parameters we have that δ i = | mx i + c- y i | is the error of the approximation for pair ( x i , y i ). For a perfect approximation we would have δ i = 0 for all i . One option is to find a line that minimizes the sum of errors δ i . This is achieved by solving min m,c 4 X i =1 | mx i + c- y i | . (1) Another option is to find a line that minimizes the maximum of errors δ i . This is achieved by solving min m,c max i =1 ,..., 4 | mx i + c- y i | . (2) 1. Formulate a linear programming problem to find...
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This homework help was uploaded on 04/18/2008 for the course ISYE 3133 taught by Professor Juanpablovielma during the Spring '08 term at Georgia Tech.
- Spring '08