Question: 5 Sensitivity analysis and the dual Consider the tables below showing data for a sensitivity analysis: 5.1 Variable X1 X2 5.2 Shadow Constraint Slack/Surplus. Price

5 Sensitivity analysis and the dual Consider the

5 Sensitivity analysis and the dual Consider the tables below showing data for a sensitivity analysis: 5.1 Variable X1 X2 5.2 Shadow Constraint Slack/Surplus. Price 395.000 0.000 0.000 0.750 0.000 0.700 C1 C2 C3 Reduced Value Cost 456.000 0.000 510.000 0.000 Objective Coefficient Ranges (Variables) Variables Lower Limit Current Values Upper Limit Allowable Increase Allowable Decrease 2.906 No limit X1 X2 C1 C C3 0.000 2.400 2.250 3.100 Right Hand Side Ranges (Constraints) Constraints Lower Limit Current Values 6,015.000 1,632.000 0.000 6,500.000 3,000.000 510.000 3,237.000 692.308 0.656 No limit Upper Limit Allowable Increase Allowable Decrease No limit 1X + 3X 4 2X +5X 8 X, X 20 2.250 0.700 No limit 237.000 182.308 How much can the processing hours in constraint 2 (c2) be increased at what cost? Identify, then write the sensitivity ranges for the objective function coefficients and the constraint quantity values. 5.3 What do the values in question 5.2 mean in terms of the optimal solution mix? 5.4 Formulate the dual for the following linear programming model: Maximise profit= 80X, +75X Subject to: 395.000 1,368.000 510.000 (3) (5) (2)

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