BUSOBA 2321 FINAL 103 ACTUAL QUESTIONS AND
ANSWERS WITH COMPLETE SOLUTION
What question are we trying to answer when performing sensitivity analysis?
Answer - How sensitive is our solution to changes in the assumptions that we
made?
T or F: The optimal solution will not always be at a corner point Answer - 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.
Answer - True
Define shadow price Answer - 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? Answer - 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? Answer - 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? Answer - 1. adjustable cells
2. constraints
For what type of constraint (what sign) might slack exist? Answer - maximums;
<
For what type of constraint (what sign) might surplus exist? Answer -
Minimums
>
Why might the allowable increase of a constraint be infinite? Answer - 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? Answer - 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? Answer - 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? Answer -
infinity
If slack exists, what is the allowable increase for the constraint? Answer -
infinity
If slack exists, what is the allowable decrease for the constraint? Answer - 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 Answer - a non-zero value
When a constraint is not binding, the shadow price is Answer - zero
For what reasons might the optimal solution omit one of the decision variable
(i.e. produce zero) Answer - 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 Answer - 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)
ANSWERS WITH COMPLETE SOLUTION
What question are we trying to answer when performing sensitivity analysis?
Answer - How sensitive is our solution to changes in the assumptions that we
made?
T or F: The optimal solution will not always be at a corner point Answer - 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.
Answer - True
Define shadow price Answer - 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? Answer - 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? Answer - 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? Answer - 1. adjustable cells
2. constraints
For what type of constraint (what sign) might slack exist? Answer - maximums;
<
For what type of constraint (what sign) might surplus exist? Answer -
Minimums
>
Why might the allowable increase of a constraint be infinite? Answer - 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? Answer - 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? Answer - 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? Answer -
infinity
If slack exists, what is the allowable increase for the constraint? Answer -
infinity
If slack exists, what is the allowable decrease for the constraint? Answer - 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 Answer - a non-zero value
When a constraint is not binding, the shadow price is Answer - zero
For what reasons might the optimal solution omit one of the decision variable
(i.e. produce zero) Answer - 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 Answer - 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)
