PLEASE DO NOT USE AI PLEASE GIVE EXPLANATION if ai is used i will report the account OPTIMIZATION: 5. The following tableau is an optimal LP tableau where X4, X5, x6 were the original slack variables. Show your work for all the questions below. Basic X1 X2 X3 X4 X5 X6 RHS Z 0 19 0 0 0 2 12 X1 1 -9 0 1 0 -1 5 X5 0 -65 0 3 -7 24 X3 0 19 1 -1 0 2 1 a. Use matrix multiplications to reconstruct the original LP and then compute the optimum objective value. b. Suppose the constraint x1 + 10x2 + x3 5 is added to the original problem. Use matrix multiplication to show how the final tableau would change (hint: this new constraint replaces one of the pre-existing constraints). If this tableau is not optimal, conduct a pivot to get a new final tableau. C. Now, in addition to the change with (b), suppose the original objective function changed to 2x1 + X2 + 3x3. Use the tableau you obtained in part (b) and matrix multiplication to show how this tableau would change. If this tableau is no longer optimum, conduct a pivot to get a new final tableau