Responses to Week 4 Poll Questions

MGMT 306

• Can you go over the Tijerina Tablets Sensitivity Analysis Problem 1?

  This problem says:

  At what minimum profit per unit should Tijerina consider producing more professional models?

  To answer this, we look at the row corresponding to the Professional Model variable in the Sensitivity Report:

  Name	Final Value	Reduced Cost	Objective Coefficient	Allowable Increase	Allowable Decrease
  Professional model	40	0	200	70	110

  We know that if the only thing that changes in the LP model is the unit profit on professional models, and the new unit profit is in the range of optimality, \([90, 270]\), then the optimal solution will stay the same. Therefore, the unit profit needs to be \(>270\) in order for Tijerina to want to produce more professional models.

  At the boundary of the range of optimality, i.e., if the unit profit is $270, Tijerina Tablets will be indifferent between producing 40 or more than 40 professional models. We will actually have alternate optimal solutions, e.g., \((M,P) = (30,40)\) and \((M,P) = (0,60)\) are both optimal achieving a profit of $16,200.

  

  

• Can you go over what the slack of a constraint is? The slack of a constraint is the (absolute value of the) difference between its left-hand-side and its right-hand-side evaluated at the optimal solution. So for example if the optimal solution is \((x,y) = (1,2)\), then the following constraints \[\begin{aligned} x + y \leq 4\\ 3x -y \geq 0\\ 2x + y = 4\\ 4x - 2 y \geq 0 \end{aligned}\] have slacks \(1, 1, 0, 0\) respectively. A constraint is binding at the optimal solution if it has 0 slack, otherwise it is non-binding. You can read the slack of a constraint from the Answer Report or Sensitivity Report. In the Answer Report, the cell value column indicates the left-hand-side of the constraint. You can compare this to the right-hand-side of your constraint to determine the slack. The slack column also reports the slack. In the Sensitivity Report, the Final Value column indicates the left-hand-side of the constraint and the Constraint R.H. Side column indicates the right-hand-side of the constraint.