Objective Coefficient Rages VariablesLoer Limit Current Value Upper Limit 10 9 4
ID: 348371 • Letter: O
Question
Objective Coefficient Rages VariablesLoer Limit Current Value Upper Limit 10 9 4 Which of the following statements is (are) true? I. If the objective function coefficient of variable X changes from 5 to 5.5, the current optimal solution remains the same. Il If the objective function coefficient of variable X changes from 5 to 5.5 and the objective function coefficient of variable Y changes from 7 to 6.5, the current optimal solution remains the same. II If the objective function coefficient of variable X changes from 5 to 9.5 and the objective function coefficient of variable Y changes from 7 to 4, the current optimal solution remains the same. IV. If the objective function coefficient of variable X changes from 5 to 9.5 and the objective function coefficient of variable Y changes from 7 to 4, the current optimal solution may not be the optimal solution. Only I is true Only l and ll are true. Only I, Il and Ill are true. Only I, Il and IV are true.Explanation / Answer
1. Ans.: a. Only I is true.
The upper and lower limit gives us the range to which the objective coefficient of the variable can be varied, without changing the objective solution. But, these ranges are valid only if a single objective coefficient is being varied.
2. Ans.: a. there is no change in the objective function value.
If we change the value of objective coefficient of variable Y to 9, it is still within the allowable limit for that variable (upper limit = 9), hence there will be no change in the value of the objective function.
3. Ans.: 3. 325
If the constraint 1 RHS is changed from 60 to 65, we are adding 5 units of resource to the constraint. A positive dual price represents the improvement in the objective function value, if we relax or add a unit to the RHS of the constraint. Here, we are adding 5 units, and the dual price is 5, hence, the change in the objective function value will be 5 units* 5 dual price = 25. Hence the objective function value = 300+25=325.
Please note here, the RHS ranges give us the range to which we can change the RHS of the constraint without changing the dual prices (NOT objective function value) of the constraints.
4. Ans.: a. 280
The change in the value objective coefficient value of X1 from 60 to 70 is still within the allowable limit of 56 to 80; hence, there will be no change in the objective function value.
The reduced cost of the variable is positive only for variables whose objective value is 0. It shows the amount by which the objective function value will change if the variable’s objective value is made non-zero.
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