1. Evaluate the impact of making two changes to the right hand sides. Department
ID: 3270884 • Letter: 1
Question
1. Evaluate the impact of making two changes to the right hand sides. Department A now has 44 hours available and department B now has 20 hours available. Show your work and explain the impact of these changes.
2. Do you consider this solution stable? Be specific in your response. Under what conditions would this be considered stable? Under what conditions would this be considered unstable?
Range Report BOX Ranges in which the basis is unchanged: objective Coefficient Ranges: Variable x1 x2 Current Coefficient 1000.000 1200.000 Allowable Increase INFINITY 300.0000 Allowable Decrease 200.0000 INFINITY Righthand Side Ranges: Current RHS 48.00000 18.00000 40.00000 Allowable Increase INFINITY INFINITY 20.00000 Allowable Decrease 16.00000 6 . 000000 40.00000 RowExplanation / Answer
1.
If we assume that Row 2 is the constraint for Department A and Row 3 is constraint for Department B, then in the problem, Department A has 48 hours available and department B now has 18 hours available.
Now, Department A now has 44 hours available and department B now has 20 hours available. So, there is decrease in number of hours by 4 for Department A. This decrease is less than the limits of Allowable decrease of 16 hrs for department A. So there will be no impact of this change on the solution.
Similarly, there is increase in number of hours by 2 for Department B. This increase is less than the limits of Allowable increase (INFINITY) for department B. So there will be no impact of this change on the solution.
So, overall there will be no impact of these changes.
2.
The condition will be unstable when any of the below condition is satisfied.
- the number of hrs available for department A decreases by more than 16 hrs. That is, the number of hrs available for department A is less than 32 hrs. (48-16)
- the number of hrs available for department B decreases by more than 6 hrs. That is, the number of hrs available for department B is less than 12 hrs. (18-6)
- the objective coefficient of X1 decreases by more than 200. That is, the objective coefficient of X1 is less than 800 (1000-200)
- the objective coefficient of X2 increases by more than 300. That is, the objective coefficient of X2 is more than 1500 (1200+300)
If all of the above conditions does not hold, the solution will be stable.
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