Question

4. v2 v3 20 30 50 30 30 40 Assume that the starting nortwest-corner solution is optimum and assosiated optimal cost is 510 TL. The followings are known: u1-0; v1-3; u2-2, C22 - C32 1; C33 and C21 are equal. a) Find all ui ; vj; and Cij b) Determine the smallest value of Cij associated with each nonbasic variable that will maintain the optimality of the northwest-corner solution

Answer 1

North West corner method quantity

	V1	V2	V3
U1	20			20
U2	10	20		30
U3		10	40	50
	30	30	40

values

	v1=3	v2=5	v3=4
u1=0	3	5	4
u2=2	5	7	6
u3=1	3	6	5

optimal cost in question is 510L

1. 3*20=60

2. 10*5=50

3. 20*7=140

4. 10*6=60

5. 40*5=200

Total= 510

	ui	vj	cij
u3+v1	4	4	0
v2+u1	5	5	0
v3+u1	4	4	0
v3+u2	6	6	0

b)

All values of cij are 0. hence the change in any non basic variable will not affect the cost