Please show all the steps as well. (No excel please) Thanks!

Consider the following LP: max. 3x; x2 + x3 s.t. X; + x2 + x3 = 8 - xy + 2x, 56 X1, X2,43 20 Let x4 and X5 are the slack variables added to these two general constraints, respectively. Given a simplex tableau as follow: BV x1 x2 x3 X4 x's RHS Z 0 4 2 3 0 24 x 1 1 1 1 0 8 X5 0 3 1 1 1 14 (1) Find the optimal BFS. (2) Suppose the value of Cz is changed to +2. Find the updated simplex tableau with minimum computation effort. Is the solution still optimal? Why? (3) Suppose the value of Ci is changed to -3. Set up the updated simplex tableau via minimum computation effort. Is the solution still optimal? Why? If not, modify the simplex tableau to find the optimal solution. (4) Use parametric programming to find the range of c1 for which the current solution is still optimal