Question

T/F Conceptual Questions and Explanations (2 pts for a true statement, 4 pts for a false statement).

Instructions:

1. A statement is true if it is true in all cases and under all conditions. Otherwise, it is false.
2. If a statement is true, no explanation is needed.
3. If a statement is false, you need to point out the mistakes and come up with a correct statement

______ By definition, reduced costs of all decision variables in a linear program should be non-negative (zero or positive).

Explanations:

______ By definition, dual prices of all constraints in a linear program should be non-negative (zero or positive).

Explanations:

______ If the reduced cost of a decision variable (product) is 5, it means that the value of this decision variable should be zero. In order for this decision variable to be positive (attractive), its objective coefficient needs to be reduced by 5.

Explanations:

______ As long as the right-hand sides (RHS) of all constraints vary within their respective ranges, all dual prices will not change.

Explanations:

______ For a resource (≤) constraint and a (profit) maximization problem, as the right-hand side (RHS) increases, the corresponding dual price will stay the same or decrease. As a result, the objective function (profit) will either stay the same or decrease.

Explanations:

______ If the 100% rule is satisfied, then the optimal solution will not change.

Explanations:

Answer 1

By definition, reduced costs of all decision variables in a linear program should be non-negative (zero or positive) - False

By definition, dual prices of all constraints in a linear program should be non-negative (zero or positive) - False

If the reduced cost of a decision variable (product) is 5, it means that the value of this decision variable should be zero. In order for this decision variable to be positive (attractive), its objective coefficient needs to be reduced by 5 - false

As long as the right-hand sides (RHS) of all constraints vary within their respective ranges, all dual prices will not change - False

For a resource (≤) constraint and a (profit) maximization problem, as the right-hand side (RHS) increases, the corresponding dual price will stay the same or decrease. As a result, the objective function (profit) will either stay the same or decrease - False

True - if the 100% rule is satisfied, then the optimal solution will not change