Question

Here is the sensitivity solution for the problem:

		OBJECTIVE FUNCTION VALUE
		6850.0000
	VARIABLE	VALUE	REDUCED COST
	X1	100.000000	0.000000
	X2	0.000000	13.000000
	X3	175.000000	0.000000
	X4	0.000000	2.000000
	ROW	SLACK OR SURPLUS	DUAL PRICE
	2)	125.000000	0.000000
	3)	0.000000	8.000000
	4)	0.000000	−10.000000

			RANGES IN WHICH THE BASIS IS UNCHANGED:
			OBJ. COEFFICIENT RANGES
	VARIABLE	CURRENT COEFFICIENT	ALLOWABLE INCREASE	ALLOWABLE DECREASE
	X1	30.000000	INFINITY	2.500000
	X2	25.000000	13.000000	INFINITY
	X3	22.000000	2.000000	2.000000
	X4	20.000000	2.000000	INFINITY
			RIGHTHAND SIDE RANGES
	ROW	CURRENT RHS	ALLOWABLE INCREASE	ALLOWABLE DECREASE
	2	500.000000	INFINITY	125.000000
	3	1200.000000	125.000000	100.000000
	4	275.000000	25.000000	35.000000

 

Based on the Sensitivity report provided, match the best response to the following questions:

1. What is the range of optimality for variable x3?

2. What is the upper limit of the feasibility region to the RHS of row 3 constraint that will maintain the dual price of $8?

3. If the coefficient of the variable x3 increases by $1, what is the added value to the objective function total value?

4. If the current coefficient of variable X1 drops to $28, what is the value of variable X1 ?

range of optimality for the Coeficient (C) of variable x3

 

               20 <= Cx3 <= 24             

What is the upper limit of the feasibility region to the RHS of row 3 constraint that will maintain the dual price of $8?

 

               1325             

If the coefficient of variable X3 increases by $1, what is the added value to the Objective Function?

 

               175             

If the current coefficient of variable X1 drops to $28, what is the value of variable X1 ?

 

Answer 1

Using given sensitivity report :- 11 Range of optinality for Variable X3 :- Coefficient of X3 = 22 Allowable increase = 2 Allowable decrease = 2 • Range = (22-2, 22+2) = (20,24) Row 3 current RHS = 1200 Allowable increase = 125 >> Upper limit of row 3 RHS for given dual price = 1200+125 = 1325 X3 coefficient increases by 1 dollar. It is within allowable increase - Added value = increase in colffx value of 3 = 1x175 = 175 x, dry coefficient drops to 28 from 30 decrease of 2, it is within allowable decrease of 2.5. Hence, optimal solution will not chans change. Value of X, = 3p 100