1st : 4
What might a change in the RHS of a binding constraint do :
- change the optimal value of the DV's - change the slack values - change the objective function value
Slack variables are :
ALWAYS POSITIVE
How do you compute the smallest value of the objective function coefficient X1 without changing the optimal solution?
ANSWER: Coefficient - allowable decrease
If the constraint is non-binding in the final solution to a Maximization problem while the FV = 6 and the RHS Value = 10, then what is the SP, Allowable Inc. + Dec. ?
SP = 0 Allowable Increase = infinity Allowable Decrease = 4
What does a variable with a negative reduced cost in a Maximization problem signify?
- its obj func coeff must increase by that amount in order to enter the basis - it is at its simple lower bound - the obj func value will decrease by that value if the variable is increased by one unit
The Simplex Method of Linear Programming (LP) :
- moves to better and better corner point solution of the feasible region until no further objective function improvement can be achieved - considers only the extreme points of the feasible region to achieve efficiency in solving LP problems
What do the values of the Allowable Increase and Allowable Decrease tell you ?
- the values give the range over which a shadow price is accurate - the values give the ranger over which an objective function coefficient can change without changing the optimal solution - the values provide a means to recognize when alternate optimal solution exist
When the allowable increase or allowable decrease for the objective function coefficient of one or more variables is zero it indicates (in the absence of degeneracy) that :
Alternate optimal solutions exist.
What does it mean when the variable X2 has a final value of 0 and a reduced cost of 0 :
Alternative Optimal Solutions.
A variable with the final value equal to its simple lower or upper bound & with a reduced cost of zero indicates that :
An alternate optimal solution exists.
The slope of the level curve for the objective function value can be changed by :
Changing a coefficient in the objective function.
Slack :
Difference between the RHS values of the constraints & the final (optimal) value assumed by the LHS.
The Cell Value column in the Solver Answer Report shows:
Final (optimal) value assumed by each constraint cell.
When a variable is basic :
IT IS PRESENT IN THE SOLUTION.
The absolute value of the SP indicates the amount which the objective function will be :
Improved if the corresponding constraint is loosened.
If the allowable increase for a constraint is 100 and we add 110 units of the resource what happens to the objective function value?
Increases but by unknown amount.
If the final value for X2 is 0, and the reduced cost value is -500.01, how much does X2 have to increase before it can enter the optimal solution at a strictly positive value :
It must increase a + 500.01.
Would a variable with a negative reduced cost in a Maximization problem have surplus resources?
NO
If the shadow price of a resource is 0 and 150 units of the resource are added what happens to the objective function value?
No change.
If the shadow price of a resource is 0 and 150 units of the resource are added what happens to the optimal solution?
No change.
What value does the Simplex Method use to determine if the objective function value can be improved?
REDUCED COST
A binding less than or equal to (<_) constraint in a maximization problem means :
That all of the resource represented by the constraint is consumed in the solution.
The solution to an LP problem is degenerate if :
The RHS of any of the constraints have an allowable increase or allowable decrease of zero.
The allowable decrease for a changing cell (decision variable) is :
The amount by which the objective function coefficient can decrease without changing the final optimal solution.
The allowable increase for a changing cell (decision variable) is :
The amount by which the objective function coefficient can increase without changing the optimal solution.
The allowable decrease for a constraint is:
The amount by which the resource can decrease given shadow price.
The allowable increase for a constraint it :
The amount by which the resource can increase given shadow price.
A change in the RHS of a constraint changes :
The feasible region.
A binding greater than or equal to (_>) constraint in a minimization problem means that :
The minimum requirement for the constraint has just been met.
The reduced cost for a changing cell (DV) is :
The per unit profits minus the per unit costs for that variable.
For a minimization problem, if a DV's final value is 0, and its RC is negative, what does this mean :
The variable has a non-negativity constraint.
Binding constraints have :
Zero Slack.
The shadow price of a nonbinding constraint is :
Zero.
The Simplex Method works by first :
identifying any basic feasible solution.
The coefficients in an LP model (cj, aij, bj) represent :
Numeric Constants.
