Problem 1: (Revised Simplex Algorithm) [25 points] For the following maximization problem: min s.t. 3x + X + X1 XI. X = 3 X22 2 + 2x2 S 4 X2 20 (a) (5 points) Write down the standard form of this LP problem to apply the simplex method. (b) (5 points) Assuming that the basic feasible solution is formed by the first three variables of the obtained standard form, write the corresponding simplex tableau, and describe how the parts (so- lution, RHS, reduced costs, main body) were obtained. Matrix notation can be used when needed. (c) (5 points) Which variable should be introduced into the basis and which removed? Explain why. (d) (5 points) Write down matrix E for the new iteration, and present recomputed simplex tableau. (e) (5 points) What are the dual variables for the new basis. How do the dual variables obtained here demonstrate that the obtained solution is optimal?