# Tutorial 9 - NATIONAL UNIVERSITY OF SINGAPORE Department of...

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NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA3252 Linear and Network Optimization Tutorial 9 1. Consider the following linear programming problem. min 5 x 1 - 5 x 2 - 13 x 3 s.t. - x 1 + x 2 + 3 x 3 20 12 x 1 + 4 x 2 + 10 x 3 90 x 1 , x 2 , x 3 0 Let x 4 and x 5 denote the slack variables for the respective constraints. The optimal tableau is given below: Basic x 1 x 2 x 3 x 4 x 5 Solution ¯ c 0 0 2 5 0 100 x 2 - 1 1 3 1 0 20 x 5 16 0 - 2 - 4 1 10 You are expected to conduct sensitivity analysis by independently investigating each of the following changes in the original model. For each change, use the sensitivity analysis procedure to obtain the new optimal solution and the new optimal objective value. (a) Change the right-hand side of the first constraint to b 1 = 30. (b) Change the right-hand sides to b 1 b 2 = 10 100 . (c) Change the coefficient of x 3 in the objective function to c 3 = 8. (d) Change the coefficient of x 2 in the objective function to c 2 = - 3.

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