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Exam 5: What-If Analysis for Linear Programming

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Question 1

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A shadow price reflects which of the following in a maximization problem?

A) The marginal cost of adding additional resources.
B) The marginal gain in the objective value realized by adding one unit of a resource.
C) The marginal loss in the objective value realized by adding one unit of a resource.
D) The marginal gain in the objective value realized by subtracting one unit of a resource.
E) None of the above.

F) B) and E)
G) A) and B)

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Question 2

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If the coefficient for Activity 1 in the objective function changes to $40,then the objective function value:

A) will increase by $77.80.
B) will increase by $23.
C) will increase by $30.
D) will remain the same.
E) can only be discovered by resolving the problem.

F) A) and B)
G) None of the above

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Question 3

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If the right-hand side of Resource C is increased by 40,and the right-hand side of Resource B is decreased by 20,then:

If the change to a right-hand side is within the allowable range,the solution will remain the same.

If the coefficient for Activity 2 in the objective function changes to $400,then the objective function value:

Solver Table re-solves the problem for a whole range of values of a data cell.

An optimal solution is only optimal with respect to a particular mathematical model that provides only a representation of the actual problem.

Figure -What is the formula contained in cell B14?

When a change occurs in the right-hand side values of one of the constraints,a proportional change will occur in one of the coefficients of the objective function.

If the coefficient of Activity 2 in the objective function changes to $100,then:

Whenever proportional changes are made to all the unit profits in a problem,the optimal solution will remain the same.

In a problem with 4 decision variables,the 100% rule indicates that each objective coefficient can be safely increase by what amount without invalidating the current optimal solution?

According to the 100% rule for simultaneous changes in objective function coefficients,if the sum of the percentage changes exceeds 100%,the optimal solution definitely will change.

The term "allowable range for the right-hand-side" refers to coefficients of the objective function.

Solver Table can only be used to investigate changes in a single data cell at a time.

A shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint.

If the coefficient for Activity 3 in the objective function changes to $30,then the objective function value:

Changing the objective function coefficients may or may not change the optimal solution,but it will always change the value of the objective function.

Figure -What is entered as the column input cell in the Solver Table dialogue box?

What-if analysis can: