Exam 8: Lp Sensitivity Analysis and Interpretation of Solution

Given the following linear program: MAX 5x₁ + 7x₂ s.t.x₁ < 6 2x₁ + 3x₂ < 19 x₁ + x₂ < 8 x₁,x₂ > 0 The graphical solution to the problem is shown below.From the graph we see that the optimal solution occurs at x₁ = 5,x₂ = 3,and z = 46. a.Calculate the range of optimality for each objective function coefficient. b.Calculate the dual price for each resource.

The 100% Rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%.

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?

The amount of a sunk cost will vary depending on the values of the decision variables.

Relevant costs should be reflected in the objective function,but sunk costs should not.

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.

The amount that the objective function coefficient of a decision variable would have to improve before that variable would have a positive value in the solution is the

If the range of feasibility indicates that the original amount of a resource,which was 20,can increase by 5,then the amount of the resource can increase to 25.

Output from a computer package is precise and answers should never be rounded.

When the right-hand sides of two constraints are each increased by one unit,the objective function value will be adjusted by the sum of the constraints' dual prices.

Use the following Management Scientist output to answer the questions. MIN 4X1+5X2+6X3 S.T. 1)X1+X2+X3<85 2)3X1+4X2+2X3>280 3)2X1+4X2+4X3>320 Objective Function Value = 400.000 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES a.What is the optimal solution,and what is the value of the profit contribution? b.Which constraints are binding? c.What are the dual prices for each resource? Interpret. d.Compute and interpret the ranges of optimality. e.Compute and interpret the ranges of feasibility.

Use the following Management Scientist output to answer the questions. LINEAR PROGRAMMING PROBLEM MAX 31X1+35X2+32X3 S.T. 1)3X1+5X2+2X3>90 2)6X1+7X2+8X3<150 3)5X1+3X2+3X3<120 OPTIMAL SOLUTION Objective Function Value = 763.333 OBJECTIVE COEFFICIENT RANGES RIGHT HAND SIDE RANGES a.Give the solution to the problem. b.Which constraints are binding? c.What would happen if the coefficient of x₁ increased by 3? d.What would happen if the right-hand side of constraint 1 increased by 10?

Decision variables must be clearly defined before constraints can be written.

If a decision variable is not positive in the optimal solution,its reduced cost is

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

The range of feasibility measures

An objective function reflects the relevant cost of labor hours used in production rather than treating them as a sunk cost.The correct interpretation of the dual price associated with the labor hours constraint is

Sensitivity analysis information in computer output is based on the assumption of

If the range of feasibility for b₁ is between 16 and 37,then if b₁ = 22 the optimal solution will not change from the original optimal solution.