Question

Consider the following linear program Max 5x1+5x2+3x3
St

x1+3x2+x3<=3

-x1+ 3x3<=2

2x1-x2 +2x3<=4

2x1+3x2-x3<=2

xi>=0 for i=1,2,3

Suppose that while solving this problem with Simplex method, you arrive at the following table:

	z	x1	x2	x3	x4	x5	x6	x7	rhs
Row0	1	0	-29/6	0	0	0	11/6	2/3	26/3
Row1	0	0	-4/3	1	0	0	1/3	-1/3	2/3
Row2	0	1	5/6	0	0	0	1/6	1/3	4/3
Row3	0	0	7/2	0	1	0	-1/2	0	1
Row4	0	0	29/6	0	0	1	-5/6	4/3	4/3

a)Write down the dual problem
b) In the Simplex table above, which variables are basic, which are nonbasic?
c) What is the current solution to this primary LP based on this Simplex table?
d) Using Complementary Slackness conditions, compute the dual solution corresponding to the primal solution given in the Simplex table
e) Compare the dual solution to the coefficients of the x variables in the Simplex table row 0 values. What do you observe?
f) Is this solution optimal? Why?
g) If you need to continue with the Simplex table what is the entering variable? What is the leaving variable?

Answer 1