Question

Maximize objective function P=3x+4y

subject to: x + y ≤ 7 x ≥ 0

x+4y ≤ 16 y ≥ 0

Answer 1

subject to

Iteration-1		Cj	3	4	0	0
B	CB	XB	x1	x2	S1	S2	MinRatio XB / x2
S1	0	7	1	1	1	0	7/1=7
S2	0	16	1	(4)	0	1	16/4=4
Z=0		Zj	0	0	0	0
		Zj-Cj	-3	-4	0	0

Negative minimum Zj-Cj is -4 and its column index is 2

Minimum ratio is 4 and its row index is 2

The pivot element is 4.

Entering =x2, Departing =S2,

.

Iteration-2		Cj	3	4	0	0
B	CB	XB	x1	x2	S1	S2	MinRatio XBx1
S1	0	3	(3/4)	0	1	-1/4	3/(3/4)=4
x2	4	4	1/4	1	0	1/4	4/(1/4)=16
Z=16		Zj	1	4	0	1
		Zj-Cj	-2	0	0	1

Negative minimum Zj-Cj is -2 and its column index is 1.

Minimum ratio is 4 and its row index is 1

The pivot element is 3/4.

Entering =x1, Departing =S1

Iteration-3		Cj	3	4	0	0
B	CB	XB	x1	x2	S1	S2	MinRatio
x1	3	4	1	0	4/3	-1/3
x2	4	3	0	1	-1/3	1/3
Z=24		Zj	3	4	8/3	1/3
		Zj-Cj	0	0	8/3	1/3

all  

optimal solution is arrived