BUSOBA 2321 Final Question and Answer
[2026] | UPDATED ACTUAL Exam | 100%
Verified Answers
• T or F: The optimal solution will not always be at a corner point -✓✓ False - it
always will be since this is where two constraints are maxed out - more resources =
more production = more optimal
• T or F: The assumptions made in our linear program formulation (i.e. how much
profit we will be able to make per unit of a particular product) may change based
on market conditions - which we do not have control over. -✓✓ True
• Define shadow price -✓✓ The change in the OBJ FN value if we increase one
constraint by one unit.
• By solving for the shadow price of a constrained resource, what question are we
answering? -✓✓ If we have a additional unit of the constrained resource available,
how much could our OBJ FN value increase by?
• How do we know if the addition of a constraing will result in the OBJ FN value
increases, staying the same, or decreasing? -✓✓ An additional constraint will never
increase the OBJ FN VAL.
If the constraint is redundant (i.e. it is already being adhered too; there is another
constraint that is more restrictive than this new constraint), our OBJ FN val wiull
remain the same - the feasible region will not change.
If it is not redundant (is not already being adhered to - the addition of this
constraint decreases our feasible region), our OBJ FN val will decrease
,• What are the two sections of a sensitivity report? -✓✓ 1. adjustable cells
2. constraints
• For what type of constraint (what sign) might slack exist? -✓✓ maximums;
<
• For what type of constraint (what sign) might surplus exist? -✓✓ Minimums
>
• Why might the allowable increase of a constraint be infinite? -✓✓ If slack
already exists - if we already aren't using up all of what we currently have
available, we will never gain anything by increasing the availability of the
resource.
• Why might the allowable decrease of a constraint be infinite? -✓✓ if a surplus
already exists - no matter how much the RHS of the constraint decreased, no
additional value would be added because we are already above the current
minimum - making the minimum lower would not help us.
• If surplus exists, what is the allowable increase for the constraint? -✓✓ the
amount of the surplus
if the minimum increases to our current amount of production, the constraint will
then be binding and thus the shadow price will become a non-zero value
• If surplus exists, what is the allowable decrease for the constraint? -✓✓ infinity
,• If slack exists, what is the allowable increase for the constraint? -✓✓ infinity
• If slack exists, what is the allowable decrease for the constraint? -✓✓ the amount
of the slack
decreasing by this amount will mean that we would be using all of the resource - it
would then be binding and the shadow price woudl change
• When a constraint is binding, the shadow price is -✓✓ a non-zero value
• When a constraint is not binding, the shadow price is -✓✓ zero
• For what reasons might the optimal solution omit one of the decision variable
(i.e. produce zero) -✓✓ 1. there is no constraint that requires the production of that
product
2. it has the lowest profit margin
• Provide two definitions of reduced cost -✓✓ 1. The minimum amount by which
the OFC of a DV needs to change to cause that DV to have a nonzero value (AKA
to include it in the optimal solution)
2. The amount by which the OBJ FN val would change if we were forced to
include one unit of that DV in our optimal solution rather than zero
, • T or F: the reduced cost is a value associated with a constraint. -✓✓ F - The
reduced cost is a value associated with a decision variable.
• How is the reduced cost calculated? -✓✓ marginal Cont. to OBJ FN Val -
marginal value of resources used
• What is the marginal value of the resources used by a DV? -✓✓ Sum of the
products of the # of units of the resource used in production of 1 unit of the DV
and the shadow price of that resource
• In general, under what circumstance would a DV not be included in the optimal
soluton? -✓✓ if it has a nonzero reduced cost
i.e. if what is gained by producing this product is less than the value of the
resources that would be used up in producing this product - resources that could go
towards producing a different product which contributes more heavily to the OBJ
FN Val
• What rule do we used to determine whether our sensitivity report is still valid
after changing multiple values (I.e. multible OFCs -OR- multiple RHS's)? -✓✓
100% Rule
If the Sum of change/allowable change values is less than 100%, then the shadow
prices in our sensitivity report are still valid.
• If changing multiple values at once while performing sensitivity analysis, how do
we calculate the net effect on the OBJ FN value? -✓✓ (Change in units 1)(Shadow
Price 1) + (Change in units 2)(Shadow Price 2)
[2026] | UPDATED ACTUAL Exam | 100%
Verified Answers
• T or F: The optimal solution will not always be at a corner point -✓✓ False - it
always will be since this is where two constraints are maxed out - more resources =
more production = more optimal
• T or F: The assumptions made in our linear program formulation (i.e. how much
profit we will be able to make per unit of a particular product) may change based
on market conditions - which we do not have control over. -✓✓ True
• Define shadow price -✓✓ The change in the OBJ FN value if we increase one
constraint by one unit.
• By solving for the shadow price of a constrained resource, what question are we
answering? -✓✓ If we have a additional unit of the constrained resource available,
how much could our OBJ FN value increase by?
• How do we know if the addition of a constraing will result in the OBJ FN value
increases, staying the same, or decreasing? -✓✓ An additional constraint will never
increase the OBJ FN VAL.
If the constraint is redundant (i.e. it is already being adhered too; there is another
constraint that is more restrictive than this new constraint), our OBJ FN val wiull
remain the same - the feasible region will not change.
If it is not redundant (is not already being adhered to - the addition of this
constraint decreases our feasible region), our OBJ FN val will decrease
,• What are the two sections of a sensitivity report? -✓✓ 1. adjustable cells
2. constraints
• For what type of constraint (what sign) might slack exist? -✓✓ maximums;
<
• For what type of constraint (what sign) might surplus exist? -✓✓ Minimums
>
• Why might the allowable increase of a constraint be infinite? -✓✓ If slack
already exists - if we already aren't using up all of what we currently have
available, we will never gain anything by increasing the availability of the
resource.
• Why might the allowable decrease of a constraint be infinite? -✓✓ if a surplus
already exists - no matter how much the RHS of the constraint decreased, no
additional value would be added because we are already above the current
minimum - making the minimum lower would not help us.
• If surplus exists, what is the allowable increase for the constraint? -✓✓ the
amount of the surplus
if the minimum increases to our current amount of production, the constraint will
then be binding and thus the shadow price will become a non-zero value
• If surplus exists, what is the allowable decrease for the constraint? -✓✓ infinity
,• If slack exists, what is the allowable increase for the constraint? -✓✓ infinity
• If slack exists, what is the allowable decrease for the constraint? -✓✓ the amount
of the slack
decreasing by this amount will mean that we would be using all of the resource - it
would then be binding and the shadow price woudl change
• When a constraint is binding, the shadow price is -✓✓ a non-zero value
• When a constraint is not binding, the shadow price is -✓✓ zero
• For what reasons might the optimal solution omit one of the decision variable
(i.e. produce zero) -✓✓ 1. there is no constraint that requires the production of that
product
2. it has the lowest profit margin
• Provide two definitions of reduced cost -✓✓ 1. The minimum amount by which
the OFC of a DV needs to change to cause that DV to have a nonzero value (AKA
to include it in the optimal solution)
2. The amount by which the OBJ FN val would change if we were forced to
include one unit of that DV in our optimal solution rather than zero
, • T or F: the reduced cost is a value associated with a constraint. -✓✓ F - The
reduced cost is a value associated with a decision variable.
• How is the reduced cost calculated? -✓✓ marginal Cont. to OBJ FN Val -
marginal value of resources used
• What is the marginal value of the resources used by a DV? -✓✓ Sum of the
products of the # of units of the resource used in production of 1 unit of the DV
and the shadow price of that resource
• In general, under what circumstance would a DV not be included in the optimal
soluton? -✓✓ if it has a nonzero reduced cost
i.e. if what is gained by producing this product is less than the value of the
resources that would be used up in producing this product - resources that could go
towards producing a different product which contributes more heavily to the OBJ
FN Val
• What rule do we used to determine whether our sensitivity report is still valid
after changing multiple values (I.e. multible OFCs -OR- multiple RHS's)? -✓✓
100% Rule
If the Sum of change/allowable change values is less than 100%, then the shadow
prices in our sensitivity report are still valid.
• If changing multiple values at once while performing sensitivity analysis, how do
we calculate the net effect on the OBJ FN value? -✓✓ (Change in units 1)(Shadow
Price 1) + (Change in units 2)(Shadow Price 2)
