Exam 3: Linear Programming: Sensitivity Analysis and Interpretation of Solution

A section of output from The Management Scientist is shown here. What will happen to the solution if the objective function coefficient for variable 1 decreases by 20?

​How would sensitivity analysis of a linear program be undertaken if one wishes to consider simultaneous changes for both the right-hand-side values and objective function.

Portions of a Management Scientist output are shown below. Use what you know about the solution of linear programs to fill in the ten blanks. LINEAR PROGRAMMING PROBLEM MAX 12X1+9X2+7X3 S.T. 1) 3X1+5X2+4X3<150 2) 2X1+1X2+1X3<64 3) 1X1+2X2+1X3<80 4) 2X1+4X2+3X3>116 OPTIMAL SOLUTION Objective Function Value = 336.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES

The dual price measures, per unit increase in the right hand side of the constraint,

The 100 percent rule can be applied to changes in both objective function coefficients and right-hand sides at the same time.

The dual price for a percentage constraint provides a direct answer to questions about the effect of increases or decreases in that percentage.

The 100% Rule compares

A negative dual price indicates that increasing the right-hand side of the associated constraint would be detrimental to the objective.

​Sensitivity analysis is often referred to as

A constraint with a positive slack value

There is a dual price for every decision variable in a model.

Eight of the entries have been deleted from the LINDO output that follows. Use what you know about linear programming to find values for the blanks. MIN 6 X1 + 7.5 X2 + 10 X3 SUBJECT TO 2) 25 X1 + 35 X2 + 30 X3 >= 2400 3) 2 X1 + 4 X2 + 8 X3 >= 400 END LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE 1) 612.50000 NO. ITERATIONS= 2 RANGES IN WHICH THE BASIS IS UNCHANGED:

​The cost that varies depending on the values of the decision variables is a

​The dual price for a < constraint

​How can the interpretation of dual prices help provide an economic justification for new technology?

The optimal solution of the linear programming problem is at the intersection of constraints 1 and 2. Max 2x₁ + x₂ s.t. 4x₁ + 1x₂ ≤ 400 4x₁ + 3x₂ ≤ 600 1x₁ + 2x₂ ≤ 300 x₁ , x₂ ≥ 0 ​ a.​Over what range can the coefficient of x₁ vary before the current solution is no longer optimal? b.​Over what range can the coefficient of x₂ vary before the current solution is no longer optimal? c.Compute the dual prices for the three constraints.