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Unformatted text preview: 53 Introduction to the Simplex Methodthe geometric method•only works for problems that have two variables•requires solving a system for every corner point•real problems may require hundreds of variables •and hundreds of constraints•which means astronomical numbers of corner points•making the above technique impractical•even on supercomputers•the Simplex Methodprovides an efficient procedure•for solving such large problems•we introduce some of the conceptsand vocabulary•associated with the Simplex Method•we will not show it in its entirety, due to lack of time53p. 1We use the following example (from the book):Constraints:x1+ 2x2≤323x1+ 4x2≤84x1, x2≥Objective function:P = 50x1+ 80x2Although the Simplex Methoddoes not rely on graphing, we will refer to its graphical solution:53p. 2(32,0)(28,0)(20,6)(0,16)(0,21)3x1+ 4x2= 84x1+ 2x2= 32feasible regionSLACKVARIABLES•The Simplex Methodstarts by converting our constraints•which are inequalities•into "equalities", or...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
 Spring '11
 Staff

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