Answer Happy

Question #3(34p): Suppose that we have the following DUAL-LP model: max Zd 120yı + 160y2 + 100y3 + 40y4 Subject to 2yı + 4y2 + 3y3 + y4 40 3y2 + 3y2 + 2y3 + y235 2yı + y2 + 4y3 + 44 45 91. Y2Y3, Y4 20 The optimal simplex tableau of corresponding primal LP model is given as below. 40 35 45 0 0 0 Basic Variables Quantity 5 1/2 0 1 0 10 60 10 30 45 35 1/2 2 1/2 1/2 32 1/2 1/2 0 0 0 2 4 1,500 40 35 45 0 0 5 25 0 0 0 0 5 -25 952 Based on the information given answer the following questions. a) Define the objective function of the primal model in terms of decision variables and compute the optimal value of objective function Z. b) Let S1, S2, S, and se are the slack variables. What are the values of dual variables Yu Yz. Y3, Y4? (hint: The dual variables equal the marginal value of the resources, the shadow prices c) Compute max Z, at the point given in part(b). Compare this value with Z given in part (a). d) Use the optimal simplex tableau and compute the sensitivity range for the coefficient C, for the decision variable Xs introducing A. Interpret your result. Show all your work!) e) By how much can the coefficient value of Xs decrease before the solution would change? f) Compute the value of objective function Z in the primal model at the lower sensivity range value of cz keeping the values of other decision variables as it is g) Use the optimal simplex tableau and compute the sensitivity range for 94 introducing A (the ranges for the 4th constraint quantitiy value). Interpret your result. (Show all your work!)