Solve the following linear program using the simplex algorithm. You should give the initial tableau and each further tableau produced during the execution of the algorithm. If the program has an optimal solution, give this solution and state its objective value. If it does not have an optimal solution, say why. You should indicate the highlighted row and columns in each pivot step as well as the row operations you carry out. 1. maximize 2x13x25x3 + x4 subject to x1+x22x3 + x4 ≤ 2, 3x23x33x4 ≤ 6, 3x12x22x3 + x4 ≤7, X1, X2, X3, X4 ≥ 0 2. Suppose that we are carrying out the simplex algorithm on a linear program in standard inequality form (with 3 variables and 4 constraints) and suppose that we have reached a point where we have obtained the following tableau. Apply one more pivot operation, indicating the highlighted row and column and the row operations you carry out. What can you conclude from your updated tableau? X2 X3 S1 S2 S3 S4 x1 S1 -2 0 1 1 0 0 0 3 S2 3 0 -2 0 1 2 0 6 x2 1 1 -3 0 0 1 0 2 S4 -3 0 2 0 0 -2 -20 11 −1 1 4 00-40-8