OMGT 6613 QUIZ 5D | QUESTIONS AND ANSWERS | 2026 UPDATE | 100% CORRECT.
Question 1
In the context of maximizing revenues for necklace production, what do the decision variables
typically represent?
A) The total amount of labor hours available in the workshop
B) The cost per ruby or sapphire used in production
C) The quantity of each specific type of necklace (e.g., Necklace 1 through 6) to be produced
D) The total revenue generated by the entire product line
E) The number of constraints that must be satisfied by the solution
Correct Answer: C) The quantity of each specific type of necklace (e.g., Necklace 1 through
6) to be produced
Rationale: In linear programming models used in operations management, decision
variables are the unknown quantities that the decision-maker controls. For this problem,
the manager must decide how many of each type of necklace to make to maximize revenue,
making the quantities produced the decision variables.
Question 2
Based on the provided quiz data, Necklace 3 is included in the optimal solution when
maximizing revenues for three necklaces. What does "included in the optimal solution" mean
mathematically?
A) Its revenue coefficient is the highest in the model
B) Its corresponding decision variable is equal to zero
C) Its corresponding decision variable is greater than zero
D) It is a slack variable for a binding constraint
E) It has reached its upper bound of production
Correct Answer: C) Its corresponding decision variable is greater than zero
Rationale: If a product is "made" or "included" in an optimal solution, it means the
optimization algorithm has determined that producing a positive quantity of that item
contributes to the objective (maximizing revenue) better than other alternatives, given the
constraints. This results in a non-zero value for that specific decision variable.
Question 3
When maximizing revenues for three necklaces, Necklace 6 is NOT made. This implies that:
A) Necklace 6 has a shadow price of zero
B) The reduced cost for Necklace 6 is likely positive (for a maximization problem)
C) Producing Necklace 6 would decrease the total revenue compared to the optimal mix
D) Necklace 6 uses no rubies or sapphires
E) Necklace 6 is a surplus variable
Correct Answer: C) Producing Necklace 6 would decrease the total revenue compared to the
optimal mix
Rationale: In an optimization model, if a variable is zero in the optimal solution (not made),
it indicates that the "cost" of using resources for that item (its opportunity cost) outweighs
, 2
the revenue it brings in. Forcing the production of Necklace 6 would draw resources away
from more profitable items like Necklace 3.
Question 4
Question 3 of the quiz asks for the most one should be willing to pay for additional labor and
materials, providing an answer of 1.5. What linear programming concept does this value
represent?
A) Slack variable
B) Reduced cost
C) Objective function coefficient
D) Shadow price (or Dual Value)
E) Feasible region boundary
Correct Answer: D) Shadow price (or Dual Value)
Rationale: The shadow price represents the marginal improvement in the objective function
(revenue) for a one-unit increase in the right-hand side of a constraint (resources like labor
or materials). A shadow price of 1.5 means that if the manager acquires one more unit of
the limiting resource, the total revenue will increase by 1.5 units.
Question 5
If the shadow price for additional labor and materials is 1.5, what is the maximum "premium"
(amount above the current cost) the manager should pay for one extra unit of this resource?
A) 0.00
B) 0.75
C) 1.50
D) 3.00
E) 1.5 multiplied by the number of necklaces
Correct Answer: C) 1.50
Rationale: The shadow price is the "willingness to pay" or the maximum value of an
additional unit of resource. Paying exactly 1.50 would result in a break-even scenario for
that marginal unit. Paying anything less than 1.50 results in a net increase in total
profit/revenue.
Question 6
According to Question 5 of the quiz, 10 gemologist labor hours are NOT used in the optimal
solution when three necklaces are made. This 10 represents which LP component?
A) Shadow Price
B) Slack
C) Surplus
D) Binding constraint
E) Non-negativity constraint
Correct Answer: B) Slack
Question 1
In the context of maximizing revenues for necklace production, what do the decision variables
typically represent?
A) The total amount of labor hours available in the workshop
B) The cost per ruby or sapphire used in production
C) The quantity of each specific type of necklace (e.g., Necklace 1 through 6) to be produced
D) The total revenue generated by the entire product line
E) The number of constraints that must be satisfied by the solution
Correct Answer: C) The quantity of each specific type of necklace (e.g., Necklace 1 through
6) to be produced
Rationale: In linear programming models used in operations management, decision
variables are the unknown quantities that the decision-maker controls. For this problem,
the manager must decide how many of each type of necklace to make to maximize revenue,
making the quantities produced the decision variables.
Question 2
Based on the provided quiz data, Necklace 3 is included in the optimal solution when
maximizing revenues for three necklaces. What does "included in the optimal solution" mean
mathematically?
A) Its revenue coefficient is the highest in the model
B) Its corresponding decision variable is equal to zero
C) Its corresponding decision variable is greater than zero
D) It is a slack variable for a binding constraint
E) It has reached its upper bound of production
Correct Answer: C) Its corresponding decision variable is greater than zero
Rationale: If a product is "made" or "included" in an optimal solution, it means the
optimization algorithm has determined that producing a positive quantity of that item
contributes to the objective (maximizing revenue) better than other alternatives, given the
constraints. This results in a non-zero value for that specific decision variable.
Question 3
When maximizing revenues for three necklaces, Necklace 6 is NOT made. This implies that:
A) Necklace 6 has a shadow price of zero
B) The reduced cost for Necklace 6 is likely positive (for a maximization problem)
C) Producing Necklace 6 would decrease the total revenue compared to the optimal mix
D) Necklace 6 uses no rubies or sapphires
E) Necklace 6 is a surplus variable
Correct Answer: C) Producing Necklace 6 would decrease the total revenue compared to the
optimal mix
Rationale: In an optimization model, if a variable is zero in the optimal solution (not made),
it indicates that the "cost" of using resources for that item (its opportunity cost) outweighs
, 2
the revenue it brings in. Forcing the production of Necklace 6 would draw resources away
from more profitable items like Necklace 3.
Question 4
Question 3 of the quiz asks for the most one should be willing to pay for additional labor and
materials, providing an answer of 1.5. What linear programming concept does this value
represent?
A) Slack variable
B) Reduced cost
C) Objective function coefficient
D) Shadow price (or Dual Value)
E) Feasible region boundary
Correct Answer: D) Shadow price (or Dual Value)
Rationale: The shadow price represents the marginal improvement in the objective function
(revenue) for a one-unit increase in the right-hand side of a constraint (resources like labor
or materials). A shadow price of 1.5 means that if the manager acquires one more unit of
the limiting resource, the total revenue will increase by 1.5 units.
Question 5
If the shadow price for additional labor and materials is 1.5, what is the maximum "premium"
(amount above the current cost) the manager should pay for one extra unit of this resource?
A) 0.00
B) 0.75
C) 1.50
D) 3.00
E) 1.5 multiplied by the number of necklaces
Correct Answer: C) 1.50
Rationale: The shadow price is the "willingness to pay" or the maximum value of an
additional unit of resource. Paying exactly 1.50 would result in a break-even scenario for
that marginal unit. Paying anything less than 1.50 results in a net increase in total
profit/revenue.
Question 6
According to Question 5 of the quiz, 10 gemologist labor hours are NOT used in the optimal
solution when three necklaces are made. This 10 represents which LP component?
A) Shadow Price
B) Slack
C) Surplus
D) Binding constraint
E) Non-negativity constraint
Correct Answer: B) Slack
