1. (10 points) Consider the following linear program: Using the simplex method, we have following information corresponding to a basis B at some stage: xB=(x3,x4,x1),xNB=(x2,x5),B1=100010131. (a) (2 points) Compute the current basic feasible solution and the dual multipliers corresponding to the basis B. (b) ( 2 points) Show that the present solution is not optimal. Which variable should now be introduced into the basis? (c) (2 points) Having chosen a variable to enter basis, now select a variable to leave basis and describe the selection rule. Is it possible that no variable meets the criterion of your rule? If this happens in some problem, what does that indicate about the original problem? (d) (2 points) Using (c), find the new inverse of the basis and the new dual multipliers. (e) (2 points) Write down the new basic feasible solution. Is it optimal? Explain