Operations Research

6.4-2

PLEASE DO PART A AND B FOR A THUMBS UP!

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6.4-2. Consider the model of Prob. 7.2-3. Use duality theory directly to determine whether the current basic solution remains optimal after each of the following independent changes. (a)The change in part (b) of Prob. 7.2-3 (b)The change in part (d) of Prob. 7.2-3 0,17.2-3. Consider the following problem. Maximize Z = 2x1 + 7 x2 3x3, subject to x + 3x +4, 530 * +41,- 1,510 and *20, X20, 120. By letting x4 and x5 be the slack variables for the respective constraints, the Page 275 (0) Z + 1 + (2) simplex method yields the following final set of equations: + 21, -20 (1) 3 + 3x3 + x - - 20 X1 +4x2 - ) + s -10 Now you are to conduct sensitivity analysis by independently investigating each of the following seven changes in the original model. For each change, use the sensitivity analysis procedure to revise this set of equations in tableau form) and convert it to proper form from Gaussian elimination for identifying and evaluating the current basic solution. Then test this solution for feasibility and for optimality. If either test fails, reoptimize to find a new optimal solution. (a)Change the right-hand sides to C- (b)Change the coefficients of xzto B-1 (c)Change the coefficients of Xito (a)Change the right-hand sides to (b)Change the coefficients of xzto 013 de (c)Change the coefficients of Xito HO 1- E-N 011 du (d)Introduce a new variable x6 with coefficients (e) Change the objective function to Z = X1 + 5x2 2x3. (f) Introduce a new constraint 3x1 + 2x2 + 3x3 = 25. (g)Change constraint 2 to x1 + 2x2 + 2x3 = 35