Question

Q1. (Basic Concept of the Simplex Procedure) (3 marks) This question is about the "Pivoting" step in the Simplex algorithm procedure. The step updates the Simplex tableau by pivoting on the intersection of the entering-variable column and the leaving variable row, i.e. perform EROs on the tableau to get a 1 in the pivot position, and 0s above and below it. We know that one ERO type is "Add a multiple of one row to another row." Consider that we are trying to make a nonzero element above or below the pivot position become 0. Please provide detailed explanations for the following questions. (a) Will adding a multiple of the reduced cost row (row 0) to the row in which the nonzero element exists induce a wrong solution? (b) Will adding a multiple of a constraint row other than the leaving-variable row to the row in which the nonzero element exists induce a wrong solution? (c) Is it always most efficient to add a multiple of the leaving-variable row to the row in which the nonzero element exists?

Answer 1

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