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Sensitivity Analysis In-class Exercise Lingo Model Minimize Z= 4x1+x2 min=4*x1+x2; Subject to 3x1+2x2>=6 3*x1+2+x2>=6; x1+2x2=0.8 xl>=0.8: x1.x2>=0 end 1. Which of the three constraints are exactly satisfied at the optimal solution? (binding constraints) 2. Solve the problem graphically and find the shadow prices of all constraints 3. What is the optimal solution? 4. If the RHS of first constraint is increased by 1, what would happen to current basis and objective function value? 5. If the RHS of second constraint is increased by 1, what would happen to current basis and objective function value? 6. If the RHS of third constraint is increased by 1, what would happen to current basis and objective function value? 7. If the RHS of first constraint increased to 13, what will happen to current basis and objective function value? 8. If the coefficient of xl in the objective function is increased by 1, will the optimal solution change? Will the optimal objective function value change? 9. If the coefficient of x2 is increased to 3, will the optimal solution change? Solution and Sensitivity Report from Lingo Global optimal solution found. Objective value 5.500000 Infeasibilities: 0.000000 Total solver iterations: Elapsed runtime seconds: 0.06 Model Class: LP Total variables: Nonlinear variables: Integer variables: Total constraints: Nonlinear constraints: Tota nonzeros: Nonlinear nonzeros: 2 2 Variable X1 X2 Value 1.000000 1.500000 Reduced Cost 0.000000 0.000000 Row 1 2 3 4 Slack or Surplus 5.500000 0.000000 0.000000 0.2000000 Dual Price -1.000000 -1.750000 1.250000 0.000000 Shadow prices signs are multiplied by -1 because it is a min. problem (default is max) Range Report Ranges in which the basis is unchanged: Objective Coefficient Ranges: Variable X1 X2 Current Coefficient 4.000000 1.000000 Allowable Increase INFINITY 1.666667 Allowable Decrease 2.500000 INFINITY Righthand Side Ranges: Row 2 3 4 Current RHS 6.000000 4.000000 0.8000000 Allowable Increase 6.000000 0.4000000 0.2000000 Allowable Decrease 0.4000000 2.000000 INFINITY Question 1 3 pts Look at the "minimization" problem and its solution report on Page 1. If the Right hand side (RHS) of the second constraint is increased by 0.4, what happens to the current basis? Basis will stay optimum, same point will be the optimal solution Basis will change, another extreme point will be the optimal solution Question 2 4 pts Look at the "minimization" problem and its solution report on Page 1. If the RHS of the second constraint is increased by 0.4, what would be the new objective function (z) value? z will decrease by 0.4 1.25 z will increase by 0.4*1.25 optimal z value will stay the same Question 3 3 pts Look at the "minimization" problem and its solution report on Page 1. If the coefficient of x1 in the objective function is increased by 1, will the optimal solution and the objective function change? Current solution will stay optimal since change is within allowable limit, but z will increase by 1x1 current solution and z value will not change since the change in the coefficient is within limits O current solution and z value will not change since the change in the coefficient is not within limits