PLEASE GO SLOW AND SHOW ME STEPS I AM TRYING TO UNDERSAND AN

PLEASE GO SLOW AND SHOW ME STEPS I AM TRYING TO UNDERSAND AND LEARN!!!!!!

Consider that after two iterations of the simplex method, you obtained the following simplex tableau:

a. What is the current basis?

b. What is the current BFS?

c. If s1, s2, and s3 are the slack variables in the augmented formulation of this problem, what is the value of the current solution? What is the value of the objective function at the current solution?

d. What is the conclusion of the optimality test for the current solution?

e. If you concluded in part d. that the current solution is not optimal or that multiple optimal solutions exist, complete one more iteration of the simplex method? What is the conclusion of the optimality test for the new solution?

Solution

(a) Since basic variables on the given pivot table are Z, x1, x2 and s3, therefore, current basis for the given pivot table is {Z, x1, x2, s3}

(b) Current basic feasible solution can be obtained by checking the right hand sides corresponding to the basic variables and considering all remaining entries as zero. Therefore, current BFS is:

Z = 3

x1 = 4

x2 = 1

s1 = 0

s2 = 0

s3 = 11

(c) Current solution of the given pivot table is x1=4, x2=1 and value of objective function at this current solution is 3

(d) We need to have the last row as well in order to perform further iterations.