True or false? ______ If the reduced cost of a variable is 5, then the objective

Question

True or false?

______ If the reduced cost of a variable is 5, then the objective function coefficient of that variable needs to be reduced by 5 to make it attractive.

______ If an LP has multiple optimal solutions, then all solutions, even though different, will lead to the same objective function value (such as total profit or cost).

______ For a maximization LP problem, additional resource (increasing the RHS of a <= constraint) may improve the objective value. But for a minimization problem, additional resource may hurt the objective value.

______ The dual price for a <= constraint will increase or stay the same as you acquire more resources (increase the RHS).

______ While a dual price can be positive or negative, a reduced cost should always be non-negative in the LINDO output.

______ As long as all prices (objective coefficients) change within their respective ranges, the optimal solution of a linear program does not change.

______ If several RHS changes do not satisfy the 100% rule, then the dual prices of these constraints will change.

______ A linear program will always have a solution but sometimes the solution may consist of non-integers.

______ If a constraint is not tight then its dual price has to be zero. This conclusion is true for both >= and <= constraints.

______ It could happen that a small change in a RHS leads to neither the optimal solution change nor the objective function value change.

______ It could happen that a small change in an objective coefficient leads to neither the optimal solution change nor the objective function value change.

Explanation / Answer

Relaxing one unit of a constraint would mean an increase in RHS in a < constraint and a decrease in RHS in a > constraint. Now in case of a non-tight or non-binding constraint, the relaxation in the constraint will not have any effect because the constraint was already not fully utilized and therefore whether it is a minimization or a maximization problem, the improvement in objective function will be zero and hence dual price will be zero.

10. True – This can happen in case of non-tight constraints and changing the constraint might not change neither optimal solution nor the objective function value.

11. True – Yes, it can happen if from the sensitivity analysis report, the change in the objective coefficient is within the allowable decrease and allowable increase range. If you are changing the value of the coefficient of the basic variable of the solution the optimal solution as well as the objective function value won’t change

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.