4. (12+6+8=26 pts) Given the following linear programming problem: max z = 4x1 + 3x2 + x3 + 2x4 s.t. 4x1 + 2x2 + x3 + x4 0 (0) Let 81, 82 denote the slack variables for the constraints (1) and (2), respectively. After applying the simplex algorithm, a portion of the final simplex tableau is as follows (22, 44 are basic variables, and RHS denotes Right-Hand Side): 2 21 X2 13 24 $1 S2 RHS Basic Variables 1 2 = 0 1 -1 2 12 = 24 = 0 -1 (1) Identify and fill the missing numbers in the final simplex tableau, without performing simplex iterations. Show your calculations. (2) What is the shadow price (dual optimal solution) for each of the constraints? (3) Suppose the coefficients of x4 are changed from CA CA -6-8-10 014 to a14 2 024 Is the current basic solution still feasible? Does it satisfy the optimality criterion? Show your steps. (Hint: find the new B, and check those two conditions separately)