Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the unit profit of a sapphire ring?
220
110
330
150
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the optimal objective value?
S = 2.5 , R =15 , T = 25
8156.25
18000
5001
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the shadow price of gold availability?
2
1
3.5
0
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the reduced cost of S?
The reduced cost is positive because S is at its upper bond.
The reduced cost is zero.
The reduced cost is positive because it is worth while to produce S.
The reduced cost is negative.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the shadow price of Sapphire?
130
it is a positive value and we can use it to calculate the opportunity cost.
it is a negative value.
It is zero since Sapphire availability is a non biding constraint.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the allowable increase of Sapphire availability?
it is infinite since the Sapphire availability is a slack constraint.
it is zero since Sapphire availability is a non binding constraint.
it is a positive number.
We don't know unless we see the excel output.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What is the allowable decrease of Sapphire availability?
It is zero since the Sapphire availability is a slack constraint.
It is a positive number.
42.5
It is infinite since the Sapphire availability is a slack constraint.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
Which statement is true?
The Sensitivity Analysis is not available if there is an integer constraint.
There is no alternate optimal solution in this problem because the allowable
increase of T is 1E + 30 .
The Sensitivity Analysis is available even with an integer constraint.
There is an alternate optimal solution in this problem.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
If the unit price of the royal ruby friendship band increases to $1550
The optimal solution will change and we have to resolve the problem to know the
new optimal solution.
The optimal solution will not change because the increase in profit is less than the
allowable increase.
The optimal solution will change because the increase in profit exceeds the
allowable increase.
The optimal solution will not change since we only change one parameter at a time.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
What happened if the minimum number of Tiffany Diamonds Ring obligated to sell in
the upcoming month is reduced from 25 to 20?
Unless we resolve the problem, we don't know what is the new optimal solution
and new optimal objective value.
The new optimal objective value will change, the new value is 7812.5, and we need
to resolve the problem to know the new optimal solution.
The new optimal objective value will change, the new value is 8500, and we need
to resolve the problem to know the new optimal solution.
The new optimal objective value will change, the new value is 8500, and the
optimal solution will not change.
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
By how much can the price of gold decrease without affecting the optimal solution?
1.4535 cents
1.5112 cents
1.3533 cents
1.7634 cents
Jack, a ring maker, is interested in determining which items he should make for the
upcoming month. His three most popular selections are a start sapphire cocktail ring, a
royal ruby friendship band, and a single diamond placed in a Tiffany setting. These items
require various combinations of diamonds, sapphires, rubies, and gold as indicated below.
Suppose Jack can produce a rainbow engagement ring that consists of 2 diamonds, 2
sapphire, 2 rubies, and 150 grains of gold. What is the minimum selling price at which
this new ring would have to be priced in order for it to be included in the optimal
product mix?
1636.25
1600.70
1720.11
can not tell, since decreases of two diamonds already exceed the allowable increase
of 1.66
The Formosa Air Cargo has expanded its shipping capability by purchasing 120 cargo
airplanes from a competitor that went bankrupt. The company subsequently located 40 of
the purchased airplanes at each of its shipping warehouses in Taipei, Taichung, and Tainan.
The company makes shipments from each of these warehouses to terminals in Tokyo, Soul,
and Hanoi. Each airplane is capable of making one shipment per day.
The terminal managers have each indicated their capability for extra shipments. The
manager at Tokyo can accommodate 40 additional airplanes per day, the manager at Soul
can accommodate 60 additional airplanes, and the manager at Hanoi can accommodate 50
additional airplanes.
Because of the differences in distance, products shipped, and transport rate, the profit
differs. The profit the company makes per airplane from each warehouse to each terminal is
listed in the following table.
Which of the following is true? (3%) Note, this problem could have multiple correct
answers and you have to answer this question correctly to continue to answer the next
question.
The Formosa Air Cargo has expanded its shipping capability by purchasing 120 cargo
airplanes from a competitor that went bankrupt. The company subsequently located 40 of
the purchased airplanes at each of its shipping warehouses in Taipei, Taichung, and Tainan.
The company makes shipments from each of these warehouses to terminals in Tokyo, Soul,
and Hanoi. Each airplane is capable of making one shipment per day.
The terminal managers have each indicated their capability for extra shipments. The
manager at Tokyo can accommodate 40 additional airplanes per day, the manager at Soul
can accommodate 60 additional airplanes, and the manager at Hanoi can accommodate 50
additional airplanes.
Because of the differences in distance, products shipped, and transport rate, the profit
differs. The profit the company makes per airplane from each warehouse to each terminal is
listed in the following table.
Present the network graph and write down the complete formulation including decision
variables, objective function, and constraints. (10%)
Tsing Hua Energy (THE) is attempting to deicide if it should introduce a new
alternative energy called Galaxy Power. The company can test market the Galaxy Power in
selected geographic areas or by pass the test market and introduce the product nationally. If
the company conducts the test market, it must wait to see the results before deciding
whether or not to introduce the Galaxy Power nationally. The probability of a positive test
market result is estimated to be 0.6. Alternatively, the company cannot conduct the test
market and make the decision to introduce the Galaxy Power or not. If the Galaxy Power is
introduced nationally and are a success, the company estimates it will realize an annual
profit of $1.6 million dollars while if the Galaxy Power fail, it will incur a loss of 0.7
million dollars.
The company believes the probability of success for the Galaxy Power is 0.5 if it is
introduced without the test market. If the company does conduct the test market and it is
positive, the probability of successfully introducing the Galaxy Power increase to 0.8. If the
test market is negative and the company introduces the Galaxy Power anyway, the
probability of success drops to 0.3.
What is the expected monetary value without test market? (3%, choose the best options.
Note! You have to answer this question correctly to answer the following question.)
1600000
Nothing
450000
684000
Tsing Hua Energy (THE) is attempting to deicide if it should introduce a new
alternative energy called Galaxy Power. The company can test market the Galaxy Power in
selected geographic areas or by pass the test market and introduce the product nationally. If
the company conducts the test market, it must wait to see the results before deciding
whether or not to introduce the Galaxy Power nationally. The probability of a positive test
market result is estimated to be 0.6. Alternatively, the company cannot conduct the test
market and make the decision to introduce the Galaxy Power or not. If the Galaxy Power is
introduced nationally and are a success, the company estimates it will realize an annual
profit of $1.6 million dollars while if the Galaxy Power fail, it will incur a loss of 0.7
million dollars.
The company believes the probability of success for the Galaxy Power is 0.5 if it is
introduced without the test market. If the company does conduct the test market and it is
positive, the probability of successfully introducing the Galaxy Power increase to 0.8. If the
test market is negative and the company introduces the Galaxy Power anyway, the
probability of success drops to 0.3.
Up to how much are you willing to pay for the test market? Construct a decision tree
and explain your answer. (10%)
A company's strategy, organization, and leadership determine a company's success.
In the knowledge economy, the technology makes information more accessible and
hence less valuable.
Most organizational relationships are rooted in knowledge-based trust. This is the
highest level of trust when there is no emotional connection between the parties.
The general business strategy (such as low cost, differentiation, and focus) can also be
used by the universities in the global competition
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