Revised Simplex Method

pinki82

Use the Revised Simplex Method to find the optimal value and one
optimal solution to the problem,
Max ( x_1 - x_3 )
x_1 - 2x_2 - x_3 + x_4 <= 1
-x_1 + 4x_2 - x_3 <= 2
-x_1 - 3x_2 + x_3 <= 3
x_1, x_2, x_3, x_4 >= 0

b) Prove that the optimal value in a) is correct.
c) Why is the solution to the Dual Unique?
d) Why is it not a surprise that the dual solution is Degenerate?
e) Show that although the dual optimal solution is degenerate, there is
only one primal optimal solution.
f) Also find 6 basic Feasible Solutions.





My work: FOr part a, i got optimal value as 4 and optimal solution x_1=4,
x_2 = 3/2 , x_3 = 0 , x_4 = 0

But i dont understnad how to do other ones..
any hint or help on any one of them please..thanks a lot!