Consider the following linear programming problem,

max 6x + 4y + 8z

s.t. : 0.02x + 0.02y + 0.04z 12

0.03x + 0.02y + 0.02z 14

0.02x + 0.01y + 0.02z 16

x,y,z 0.

Final simplex tableau

		x	y	z	s1	s2	s3
basis	Cb	6	4	8	0	0	0
z	8	0	0.25	1	37.5	-25	0	100
x	6	1	0.5	0	-25	50	0	400
s3	0	0	-0.005	0	-0.25	-0.5	1	6
zj		6	5	8	150	100	0	3200
cj - zj		0	-1	0	-150	-100	0

i)Perform one iteration of the simplex method toward solving the problem. Initial simplex is not counted as an iteration.

ii) what is the optimal solution found by simplex method?

iii) what is the optimal value of the problem ?

iv) How many constraints are binding ? why?

v) what is the change in the optimal value of the problem if we increase RHS of the first constraint from 12 to 13?

vi) Find the allowable increase and allowable decrease of the coefficient of x in the objective function.