sensitivity - Example Sensitivity Analysis 1 p 346 number 3...

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Example Sensitivity Analysis 1 p 346 number 3 The original LP: max z = 5 x 1 + x 2 + 2 x 3 s.t. x 1 + x 2 + x 3 6 6 x 1 + x 3 8 x 2 + x 3 2 x 1 , x 2 , x 3 0 The optimal tableau: Z x 1 x 2 x 3 s 1 s 2 s 3 rhs 1 0 1 6 0 0 5 6 7 6 9 s 1 0 0 1 6 0 1 - 1 6 - 5 6 3 x 1 0 1 - 1 6 0 0 1 6 - 1 6 1 x 3 0 0 1 1 0 0 1 2 We want to find out what are the ranges of the objective coefficients of x 1 and x 2 that keep the current basic feasible solution optimal. In other words, how much can I change the coefficients of x 1 and x 2 but still have non-negative entries in my row zero? Recall, the formula for the row zero entry of variable i : ˆ c i = c BV B - 1 a i - c i where c BV is the vector of original objective coefficients of the basic variables, B is the matrix containing the constraint coefficients from the original formulation of the basic variables, a i is the vector of constraint coefficients for the ith variable, and c i is the original objective coefficient of the ith variable.
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