Question

Label each of the following statements as True or False

1) If no slack or surplus variable is needed to convert a primal constraint to an equation, the corresponding dual variable will necessarily be unrestricted.

2) If a surplus variable is used to convert a primal constraint to an equation, the corresponding dual variable will be unrestricted regardless of whether the primal is
maximization or minimization.

3) The addition of a new activity can improve the objective value.

4) In an LP, it is possible to change the coefficients of the objective function without changing the optimal values of the variables.

Answer 1

1.slack variables:The  variables which are added to the constraints in LP to convert the inequalities of less than or equal to type to equations are called slack variables

surplus variables: The variables which are subtracted from the constraints of greater than or equal to type to equations are called surpplus variables.

I no slack or surplus variable needed to convert the primal constraint to an equation means the constraint is an equation. The the corresponding dual variable will be unrestricted .

Therefore the given statement is true.

2.If a surplus variable is used in primal to convert the constraint to an equation that means the primal is a minimazation problem.That means the dual is a maximization problem and the inequality in dual will be of less than or equal to type .Therefore the corresponding variable is not unrestricted.

hence the second statement is false.

3. Addition of new activity means addition of a new variable to the objective function which means there is an improvement in the objective function or the objective function is unchanged .Therefore the statement is true .

4. Yes in the LP it is possible to change the coefficients of the objective without changing the optimal values of the

variables.Therefore the statement 4 is true and this study is called sensivity analysis