2. Consider the following LP: max. 3x1 x2 + x3 - s.t. x1+x2+x38 -x1 + 2x2 6 X1, X2, X3 0 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 X5 RHS Z 0 4 2 3 0 24 X1 1 1 1 1 0 8 X5 0 3 1 1 1 14 (1) Find the optimal BFS. (10pts) (2) Suppose the value of c3 is changed to +2. Find the updated simplex tableau with minimum computation effort. Is the solution still optimal? Why? (10pts) (3) Suppose the value of cl is changed to -3. Set up the updated simplex tableau via minimum computation effort discussed in our MS class. Is the solution still optimal? Why? If not, modify the simplex tableau to find the optimal solution. (10pts) (4) Use parametric programming to find the range of cl for which the current solution is still optimal. (10pts)