Deck 5: What-If Analysis for Linear Programming

Question 1

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

Answer 1

False

Question 2

The purpose of a linear programming study is to help guide management's final decision by providing insights.

Answer 2

True

Question 3

It is usually quite easy to find the needed data for a linear programming study.

Answer 3

False

Question 4

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

Question 5

The term "allowable range for an objective function coefficient" refers to a constraint's right-hand side quantity.

Question 6

Every change in the value of an objective function coefficient will lead to a changed optimal solution.

Question 7

If the optimal solution will remain the same over a wide range of values for a particular coefficient in the objective function,then management will want to take special care to narrow this estimate down.

Question 8

When maximizing profit in a linear programming problem,the allowable increase and allowable decrease columns in the sensitivity report make it possible to find the range over which the profitability does not change.

Question 9

A shadow price tells how much a decision variable can be increased or decreased without changing the value of the solution.

Question 10

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

Question 11

Shadow price analysis is widely used to help management find the best trade-off between costs and benefits for a problem.

Question 12

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.

Question 13

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.

Question 14

If the change to a right-hand side is within the allowable range,the value of the shadow price remains valid.

Question 15

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

Question 16

The allowable range gives ranges of values for the objective function coefficients within which the values of the decision variables are optimal.

Question 17

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

Question 18

When certain parameters of a model represent managerial policy decisions,what-if analysis provides information about what the impact would be of altering these policy decisions.

Question 19

When a change in the value of an objective function coefficient remains within the allowable range,the optimal solution will also remain the same.

Question 20

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

Question 21

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

Question 22

Solver Table can be used to easily investigate the changes in any number of data cells.
Multiple Choice Questions

Question 23

Which of the following are benefits of what-if analysis?

A)It pinpoints the sensitive parameters of the model.
B)It gives the new optimal solution if conditions change.
C)It tells management what policy decisions to make.
D)All of the above.
E)None of the above.

Question 24

In linear programming,what-if analysis is associated with determining the effect of changing: I.objective function coefficients.
II)right-hand side values of constraints.
III)decision variable values.

A)I and II
B)II and III
C)I,II,and III
D)I and III
E)None of the above.

Question 25

What-if analysis can:

A)be done graphically for problems with two decision variables.
B)reduce a manager's confidence in the model that has been formulated.
C)increase a manager's confidence in the model that has been formulated.
D)All of the above.
E)a.and c.only.

Question 26

Figure

-What is the allowable range for changes in the right-hand-side for Resource C?

A)18 $\le$ RHS_c $\le$ $\infty$ .
B) $\infty$ $\le$ RHS_c $\le$ 62.
C)-2 $\le$ RHS_c $\le$ $\infty$ .
D)- $\infty$ $\le$ RHS_c $\le$ 40.
E)0 $\le$ RHS_c $\le$ 22.

Question 27

When even a small change in the value of a coefficient in the objective function can change the optimal solution,the coefficient is called:

A)optimal.
B)sensitive.
C)out of the range.
D)within the range.
E)None of the above.

Question 28

If the sum of the percentage changes of the right-hand sides does not exceed 100%,then the solution will definitely remain optimal.

Question 29

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.

Question 30

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

A)will increase by $70.
B)is $0.
C)will increase by $30.
D)will remain the same.
E)will increase by an unknown amount.

Question 31

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?

A)25%.
B)25% of the allowable increase of that coefficient.
C)100%.
D)25% of the range of optimality.
E)It can't be determined from the information given.

Question 32

If the right-hand side value of a constraint in a two variable linear programming problems is changed,then:

A)the optimal measure of performance may change.
B)a parallel shift must be made in the graph of that constraint.
C)the optimal values for one or more of the decision variables may change.
D)All of the above.
E)None of the above.

Question 33

What-if analysis:

A)may involve changes in the objective function coefficients.
B)requires that only one parameter change while the rest are held fixed.
C)may involve changes in the right-hand side values.
D)All of the above.
E)None of the above.

Question 34

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.

Question 35

Figure

-What is the allowable range for changes in the objective coefficient for Activity 2?

A)-10 $\le$ A2 $\le$ 50.
B)-44 $\le$ A2 $\le$ 16.
C)-4 $\le$ A2 $\le$ 56.
D)30 $\le$ A2 $\le$ 90.
E)20 $\le$ A2 $\le$ 80.

Question 36

If a change is made in only one of the objective function coefficients:

A)the slope of the objective function line always will change.
B)the optimal solution always will change.
C)one or more of the decision variables always will change.
D)All of the above.
E)None of the above.

Question 37

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.

Question 38

Figure
What is the optimal objective function value for this problem?

A)It cannot be determined from the given information.
B)$7.78.
C)$240.
D)$90.
E)$330.

Question 39

Managerial decisions regarding right-hand sides are often interrelated and so frequently are considered simultaneously.

Question 40

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

Question 41

If the right-hand side of Resource C changes to 140,then the objective function value:

A)will increase by $137.50.
B)will increase by $57.50.
C)will increase by $80.
D)will remain the same.
E)can only be discovered by resolving the problem.

Question 42

If the right-hand side of Resource B changes to 80,then the objective function value:

A)will decrease by $75.
B)will decrease by $150.
C)will decrease by $225.
D)will remain the same.
E)can only be discovered by resolving the problem.

Question 43

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

A)will increase by $7,500.
B)will increase by $2,750.
C)will increase by $100.
D)will remain the same.
E)can only be discovered by resolving the problem.

Question 44

Figure
What is the optimal objective function value for this problem?

A)It cannot be determined from the given information.
B)$1,200.
C)$975.
D)$8,250.
E)$500.

Question 45

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:

A)the optimal solution remains the same.
B)the optimal solution will change.
C)the shadow price is valid.
D)the shadow price may or may not be not valid.
E)None of the above.

Question 46

Which parameter is most sensitive to an increase in its value?

A)The objective coefficient of Activity 1.
B)The objective coefficient of Activity 2.
C)The objective coefficient of Activity 3.
D)All of the above.
E)None of the above.

Question 47

If the right-hand side of Resource A changes to 10,then the objective function value:

A)will decrease by $12.50.
B)will decrease by $125.
C)will decrease by $77.80.
D)will remain the same.
E)can only be discovered by resolving the problem.

Question 48

If the coefficients of Activity 1 and Activity 2 in the objective function are both increased by $10,then:

A)the optimal solution remains the same.
B)the optimal solution may or may not remain the same.
C)the optimal solution will change.
D)the shadow prices are valid.
E)None of the above.

Question 49

If the right-hand side of Resource B is increased by 30,and the right-hand side of Resource C is decreased by 10,then:

A)the optimal solution remains the same.
B)the optimal solution will change.
C)the shadow prices are valid.
D)the shadow prices may or may not be valid.
E)None of the above.

Question 50

If the objective coefficients of Activity 2 and Activity 3 are both decreased by $100,then:

A)the optimal solution remains the same.
B)the optimal solution may or may not remain the same.
C)the optimal solution will change.
D)the shadow prices are valid.
E)None of the above.

Question 51

If the right-hand side of Resource C changes to 130,then:

A)the original solution remains optimal.
B)the problem must be resolved to find the optimal solution.
C)the shadow price is valid.
D)the shadow price is not valid.
E)None of the above.

Question 52

If the coefficient for Activity 1 in the objective function changes to $50,then the objective function value:

A)will decrease by $450.
B)is $0.
C)will decrease by $2750.
D)will remain the same.
E)can only be discovered by resolving the problem.

Question 53

If the right-hand side of Resource B changes to 10,then:

A)the original solution remains optimal.
B)the problem must be resolved to find the optimal solution.
C)the shadow price is valid.
D)the shadow price is not valid.
E)None of the above.

Question 54

If the right-hand side of Resource B changes to 10,then the objective function value:

A)will decrease by $120.
B)will decrease by $60.
C)will decrease by $20.
D)will remain the same.
E)can only be discovered by resolving the problem.

Question 55

Solver Table can be used to investigate the changes in how many data cells at a time?

A)1
B)2
C)3
D)All of the above.
E)a or b.

Question 56

Figure

-What is the allowable range of the right-hand-side for Resource A?

A)- $\infty$ $\le$ RHS_A $\le$ 60.
B)0 $\le$ RHS_A $\le$ 110.
C)- $\infty$ $\le$ RHS_A $\le$ 110.
D)110 $\le$ RHS_A $\le$ 1600.
E)0 $\le$ RHS_A $\le$ 160.

Question 57

Figure

-What is the allowable range for the objective function coefficient for Activity 3?

A)150 $\le$ A3 $\le$ $\infty$ .
B)0 $\le$ A3 $\le$ 650.
C)0 $\le$ A3 $\le$ 250.
D)400 $\le$ A3 $\le$ $\infty$ .
E)300 $\le$ A3 $\le$ 500.

Question 58

If the coefficient of Activity 1 in the objective function changes to $10,then:

A)the original solution remains optimal.
B)the problem must be resolved to find the optimal solution.
C)the shadow price is valid.
D)the shadow price is not valid.
E)None of the above.

Question 59

Figure
Which cells in the following spreadsheet must be selected before choosing Solver Table from the Tools menu?

A)A15:D19
B)A14:D19
C)A12:D19
D)B2
E)B8:C8 and F8

Question 60

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

A)the original solution remains optimal.
B)the problem must be resolved to find the optimal solution.
C)the shadow price is valid.
D)the shadow price is not valid.
E)None of the above.

Question 61

Figure
What is the formula contained in cell B14?

A)= B2
B)= B8
C)= C2
D)= C8
E)None of the above.

Question 62

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

A)B2
B)B8
C)F5
D)F8
E)It is left blank.

Question 63

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

A)B2
B)B8
C)F5
D)F8
E)It is left blank.