Question 1 Match the following sensitivity parameters to the appropriate definit
ID: 431290 • Letter: Q
Question
Question 1
Match the following sensitivity parameters to the appropriate definition
Shadow Price
Reduced Cost
Objective Function Coefficient Changes
Resource Function Changes
A.
Represents the change required to an objective function coefficient of non basic variable that will make the variable basic
B.
Causes constraints to shift parallel from its original position
C.
Represents the unit value increase/decrease in profit as a result of increasing the resource
D.
Causes change in the slope of the iso profit (objective function ) line
Question 2
Sensitivity Analysis in Linear programming problems
1.
Indicates the effect of changes in the problem data
2.
Can tell the decision maker if the current optimal solution will remain so if an objective function coefficient changes
3.
Can provide the worth of additional resources
4.
All of the above
5.
None of the above
Question 3
Assume the shadow price for a given resource of a maximization problem is 16. On this basis, what would be most beneficial option for company ABC
1.
Increases resources to allowable level if unit price of resource is $20
2.
Increases resources to allowable level if unit price of resource is $12
3.
Decreases resources to allowable level if unit price of resource is $20
4.
Increases resources to allowable level if unit price of resource is $22
Question 4
Refer to problem 2 on page 254 of the text (Vivian s Gems) What would Vivian s profit be if 35 rubies were available?
1.
$71
2.
$59
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Question 5
Refer to problem 2 on page 254 of the text (Vivian s Gems) If type 2 gems sold for only $5.50, what would be the new optimal solution to the problem
1.
$64
2.
$60
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Question 6
Refer to problem 2 on page 254 of the text (Vivian s Gems). What would Vivian s profit be if at least 12 type 1 gems had to be produced?
1.
$64
2.
$60
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Question 7
Refer to problem 2 on page 254 of the text (Vivian s Gems). A vendor offers to sell 2 diamonds at a cost of $1 above current prices. What would Vivian s new profit be given Vivian accepts the offer?
1.
$64
2.
$60
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Question 8
Refer to problem 2 on page 254 of the text (Vivian s Gems)14. If type 1 gems sold for only $15, what would be the new optimal solution to the problem?
1.
$64
2.
$60
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Question 9
Refer to problem 2 on page 254 of the text (Vivian s Gems) What would Vivian s profit be if 46 diamonds were available?
1.
$71
2.
$59
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Question 10
In a report of sensitivity analysis in a lindo LP output, if the original objective function coefficient is 6 and the allowable increase is 2.4, then if the coefficient were to become 7, there would be no change in the optimal values of the variable
1.
true
2.
false
Question 11
The results of sensitivity analysis establish ranges for the decision variables within which the current solution remains optimal
1.
true
2.
false
Question 12
It is possible, after a change in an objective function coefficient, to have an optimal solution with the same value for the decision variables but a different value for the objective function
1.
true
2.
false
Question 13
Right hand side sensitivity reveals provides details in the limitation of variable values that will cause changes in the RHS
1.
true
2.
false
Question 14
It has been determined that the optimal solution of a linear programming problem occurs at the intersection of the constraint lines 5x1 + 3x2 = 300 and 4x1 + 9x2 = 600. What can be said about the objective function with regards to sensitivity analysis
1.
The constraints are maximized
2.
Its optimal value cannot exceed 600
3.
The slope is between -5/3 and -4/9
4.
The problem is infeasible
Question 15
If sensitivity analysis shows an allowable increase of infinity for the objective coefficient range for variable x1, it means
1.
The problem is unbound
2.
The value of x1 can increase without limit
3.
The objective function coefficient for x1 can increase without limit and variables will all have the same optimal values
4.
The objective function coefficient for x1 can increase without limit and all the variables except x1 will change their optimal value
Question 16
The objective function Max 14x1 + 19x2 reflects the relevant cost of labor hours used in production. The correct interpretation of shadow price associated with the labor hours constraint is
1.
The maximum premium over the normal price (say for overtime) the company would be willing to pay.
2.
The upper limit on the total hourly wage the company would be willing to pay
3.
The reduction in hours that could be sustained before the solution would change
4.
All of the above
5.
None of the above
Question 17
Suppose the shadow price for resource 1 in an LP problem is 22. Also, consider that the constraint that establishes the resource requirement is a "less than or equal to" type constraint. As such, there is no slack ( or "zero" value for slack) associated with the constraint of resource 1.
1.
true
2.
false
Here is the link for question on page 254 https://www.chegg.com/homework-help/operations-research-applications-and-algorithms-4th-edition-chapter-5.4-problem-2rp-solution-9780534380588?trackid=0e601d54&strackid=6f8eff6c&ii=1
Shadow Price
Explanation / Answer
Question 1
Reduced cost
A. Represents the change required to an objective function coefficient of non basic variable that will make the variable basic
Resource function changes
B. Causes constraints to shift parallel from its original position
Shadow price
C. Represents the unit value increase/decrease in profit as a result of increasing the resource
Objective function coefficient changes
D. Causes change in the slope of the iso profit (objective function ) line
Question 2. (4) All of the above
Question 3. (2) Increases resources to allowable level if unit price of resource is $12
Shadow price of 16 means that each additional unit of resource will increase the objective value by 16. Therefore, increasing the resources to allowable level at a unit cost of $ 12 will lead to a profit of 16-12 = $ 4 for each additional unit of resource.
Question 4. to 9 are based on problem Vivian's gems, which is not given in the question.
Question 10. (1) True
Change from 6 to 7 is only 1, which is less than the allowable increase of 2.4. Therefore, there would be no change in the optimal values of the variables.
Reduced cost
A. Represents the change required to an objective function coefficient of non basic variable that will make the variable basic
Resource function changes
B. Causes constraints to shift parallel from its original position
Shadow price
C. Represents the unit value increase/decrease in profit as a result of increasing the resource
Objective function coefficient changes
D. Causes change in the slope of the iso profit (objective function ) line
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