In each case given below, there are two optimization problems with optimal objective values z and w respectively. You can assume that both the problems are feasible and bounded. In each case, select the MOST correct one answer and provide explanation. If no explanation is provided, you will get 0 score. (1) (2) (3) (a) z w (b) z > w relationship between z and w. 2x13x2 +4x3 s.t. 421 +32 +3 4 1 + x2 +93 2 11, 12, 13 20 91.92 20 (c) 2 = w (d) There is not enough information to obtain a z = min s.t. z = max z = max s.t. (a) z w (b) z w (c) z = w relationship between z and w. (a) z w relationship 3x12x2 + x3 x1 + 5x2 + 2x3 2 -2x1 +4x2x3 4 21 0, 22, 23 20 3x12x2 -13 21+ 2x2 + 3x3 2 -21 +22-23 24 21, 220, 23 0 w = min s.t. (b) z 2 w (c) z = w between z and w. 4y1+2y2 4y1 + y2 22 3y + y22-31 w = min s.t. 4x12x2 x1 +5x2 2 -2x1 +4x224 21 0,22 0 (d) There is not enough information to obtain a w = max 3x12x2x3+ (2x2 - 3 - 3) s.t. -1 + 2x2 - 3 4 1,2 20,3