Here is the link for question on page 254 https://www.chegg.com/homework-help/op
ID: 431694 • Letter: H
Question
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
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 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
1.
$64
2.
$60
3.
$67
4.
Cannot determine since the change is outside the range of optimality
5.
None of the above
Explanation / Answer
5.
The allowable decrease of the objective coefficient of X2 is 0.75. Here the proposed decrease is 0.50 only which is less than the allowable decease. So, no change will be observed in the optimal values. The objective value will be:
11 x 5 + 6 x 1.5 = $64
6.
For the last constraint, the dual price is -3.0. This dual price is valid for an allowable increase of the RHS by 1.5. Here, the proposed increase is 1 unit. So, the dual price remains the same. The profit will reduce by 3 x 1 = $3.
The new objective value will be $67 - $3 = $64
7.
For the second (diamond) constraint, the dual price is 2.0. This dual price is valid for an allowable increase of the RHS by 2. Here, the proposed increase is 2 unit. So, the dual price remains the same. The profit will increase by 2 x 2 = $4.
Additional cost incurred = $1 x 2 = $2
So, the new profit = $67 + $4 - $2 = $69
8.
The allowable increase of the objective coefficient of X1 is 3. Here the proposed increase is 5 which is more than the allowable decease. So, we cannot determine the change in optimal solution since the change is outside the range of optimality.
9.
The allowable decrease of the diamond constraint is 6. The proposed decrease is 4 units (50 - 46 = 4). So, the reduction is profit will be 4 x $2 (dual price) = $8.
So, the new objective will be $67 - $8 = $59