Answer Happy

5 Sensitivity analysis and the dual Consider the tables below showing data for a sensitivity analysis: 5.1 Variable 5.2 X1 X2 C1 C2 C3 Shadow Constraint Slack/Surplus. Price 395.000 0.000 0.000 0.750 0.000 0.700 X1 X2 Reduced Cost Value 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 C1 C₂ C3 0.000 2.400 2.250 3.100 Right Hand Side Ranges (Constraints) Constraints Lower Limit Current Values 6,015.000 6,500.000 1,632.000 3,000.000 0.000 510.000 3,237.000 692.308 Upper Limit Allowable Increase Allowable Decrease No limit 0.656 No limit 5.3 √5.4 Formulate the dual for the following linear programming model: What do the values in question 5.2 mean in terms of the optimal solution mix? Maximise profit= 80X, +75X₂ Subject to: 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. 1X₁ + 3X₂ ≤ 4 2X₁ +5X₂ ≤ 8 X₁, X₂ 20 2.250 0.700 395.000 1,368.000 510.000 (3) (5) (2) (5)