1. In Example 4.3-1, compute the change in the optimal revenue in each of the following cases (use TORA output to obtain the feasibility ranges): (a) The constraint for raw material M1 (resource 1) is 6x1 + 4x2 = 20. (b) The constraint for raw material M2 (resource 2) is xy + 2x2 5 5. (c) The market condition represented by resource 4 is x, S 4. Example 4.3-1 The Reddy Mikks model (Example 2.1-1) and its dual are given as follows: Reddy Mikks primal Maximize z = 5x + 4x2 subject to 6x + 4x2 s 24 (resource 1, MI) X; + 2x2 5 6 (resource 2, M2) --X1 + X2 51 (resource 3, market) X2 S 2 (resource 4, demand) X1, X, 20 Optimum solution: x3 = 3, x2 = 1.5, z = 21 Reddy Mikks dual Minimize w = 24y + 6y2 + y + 2y4 subject to 6y, + y2 - Y3 25 4y, + 2y2 + Y3 + y4 2 4 Yu, Y2, Yz, Y4 20 Optimum solution: y = .75, y2 = 0.5, y3 = 44 = 0, w = 21