# assignment6 - x 6 as entering variable. Do you see a...

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ORIE 3300/5300 ASSIGNMENT 6 Fall 2011 Individual work. Due: 11am, Tuesday October 18. 1. A coach must assign four swimmers to a 200-meter medley relay team. He can choose from ﬁve available swimmers, each of whom could swim the 50-meter leg in any one of the four strokes. The swimmers’ best times in each stroke are listed below (in seconds). Stroke Alan Brad Chris Dennis Eddie Backstroke 37.7 32.9 33.8 37.0 35.4 Breaststroke 43.4 33.1 42.2 34.7 41.8 Butterﬂy 33.3 28.5 38.9 30.4 33.6 Freestyle 29.2 26.4 29.6 28.5 31.1 The coach wants the fastest possible team. Explain how to formulate his task as an assignment problem, and solve it, using the AMPL model ﬁle transp.mod . 2. Consider the following tableau (written in shorthand—we write each variable above a column containing its coeﬃcients). z x 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 1 2 1 0 0 - 1 - 2 0 - 3 2 - 2 3 0 = 0 0 0 - 1 1 0 1 1 0 1 - 1 0 - 1 - 1 = 0 0 1 1 0 1 - 1 0 - 1 - 1 0 - 1 1 0 = 0 . The initial basic variables are x 3 and x 4 . Perform a pivot with x 5 as entering variable, followed by a pivot with

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Unformatted text preview: x 6 as entering variable. Do you see a pattern? Explain how the simplex method could cycle in twelve iterations, starting from the tableau above. What would happen if you used the smallest subscript rule? 3. The following claims concern a single pivot of the simplex method, from a current tableau to a new tableau. State whether each claim is true or false. Justify your answers: if you state a claim is true, explain why; if you state it is false, give an example illustrating that it can fail. (i) After a degenerate pivot, the new tableau must be degenerate. 1 (ii) Starting from a degenerate current tableau, any pivot must be degenerate. (iii) If the new tableau is degenerate, the pivot must have been degen-erate. (iv) A degenerate pivot must start from a degenerate current tableau. 2...
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## This note was uploaded on 10/31/2011 for the course OR&IE 3300 at Cornell University (Engineering School).

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assignment6 - x 6 as entering variable. Do you see a...

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