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4.10 – The Big M Method

Copyright (c) 2003 Brooks/Cole, a division of Thomson Learning, The Big M MethodLetting x1 = number of ounces of orange soda in a bottle of Oranjx2 = number of ounces of orange juice in a bottle of OranjThe LP is:min z = 2x1 + 3x2st + 4(sugar constraint) x1 + 3x2 20(Vitamin C constraint) x1 + x2 = 10(10 oz in 1 bottle of Oranj) x1, x2, > 0 The LP in standard form is shown on the next (c) 2003 Brooks/Cole, a division of Thomson Learning, The Big M MethodRow 1:z - 2x1 - 3x2 = 0 Row 2: + + s1 = 4 Row 3: x1 + 3x2 - e2 = 20 Row 4: x1 + x2 = 10 The LP in standard form hasz and s1 which could be usedfor BVs but row 2 wouldviolate sign restrictio

In order to use the simplex method, a bfs is needed. To remedy the predicament, artificial variables are created. The variables will be labeled according to the row in which they are used as seen below. Row 1:z - 2x 1 - 3x 2 = 0 Row 2: 0.5x 1 + 0.25x 2 + s 1 = 4 Row 3: x 1 + 3x 2 - e 2 + a 2 = 20 Row 4: x 1 + x 2 + a 3 = 10

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  Methods, Simplex method, Simplex

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