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

In a linear programming problem,the binding constraints for the optimal solution are: 5X + 3Y ≤ 30 2X + 5Y ≤ 20 a.Fill in the blanks in the following sentence: As long as the slope of the objective function stays between _______ and _______,the current optimal solution point will remain optimal. b.Which of these objective functions will lead to the same optimal solution? (1)2X + 1Y (2)7X + 8Y (3)80X + 60Y (4)25X + 35Y

The dual value and dual price are identical for a minimization problem.

The binding constraints for this problem are the first and second. ​ a.Keeping c₂ fixed at 2,over what range can c₁ vary before there is a change in the optimal solution point? b.Keeping c₁ fixed at 1,over what range can c₂ vary before there is a change in the optimal solution point? c.If the objective function becomes Min 1.5x₁ + 2x₂,what will be the optimal values of x₁,x₂,and the objective function? d.If the objective function becomes Min 7x₁ + 6x₂,what constraints will be binding? e.Find the dual price for each constraint in the original problem.

A constraint with a positive slack value

For a minimization problem,a positive dual price indicates the value of the objective function will increase.

Sensitivity analysis is sometimes referred to as

The range of feasibility measures

A small change in the objective function coefficient can necessitate modifying the optimal solution.

If the dual price for the right-hand side of a ≤ constraint is zero,there is no upper limit on its range of feasibility.

Classical sensitivity analysis provides no information about changes resulting from a change in the coefficient of a variable in a constraint.

In order to tell the impact of a change in a constraint coefficient,the change must be made and then the model resolved.

The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

Which of the following is NOT a question answered by standard sensitivity analysis information?

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

The graphical solution procedure is useful only for linear programs involving

Sensitivity analysis is concerned with how certain changes affect the

If the optimal value of a decision variable is zero and its reduced cost is zero,this indicates that alternative optimal solutions exist.

Based on the per-unit increase in the right-hand side of the constraint,the dual price measures the

An improvement in the value of the objective function per unit increase in a right-hand side is the

The dual price associated with a constraint is the change in the value of the solution per unit decrease in the right-hand side of the constraint.