BUSOBA 2321 Final Exam | Verified with 100% Correct Answers
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Module
BUSOBA 2321
Institution
BUSOBA 2321
BUSOBA 2321 Final Exam | Verified with 100% Correct Answers What question are we trying to answer when performing sensitivity analysis? 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 False - it always wil...
What question are we trying to answer when performing sensitivity analysis?
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
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 would 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
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