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Test_Solution - MS3401 Practical Management Science Summer...

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- 1 - MS3401 Practical Management Science Summer 2009, Mid-Term Test Suggested Solution Question 1 (25 marks) (a) Ans: AB: 3 x1 + 4 x2 <= 12 Y CD: 10 x1 + 4 x2 <= 20 Y (b) Ans: AGDO Z (c) Ans: Z = 2 Y (d) Ans: Optimal solution point: G (1.1429, 2.1429) Y Optimal value of Z = 1.1429 + 2.1429 = 3.2858 Y (e) Ans: New feasible region is ACG Y New optimal solution point: C (0, 5) Y (f) Ans: Feasible region and optimal solution point will not be affected [ (g) Ans: Since the new objective function line is parallel to CD X , and thus there exists multiple optimal solutions X . Any point in the line segment GD is an optimal solution Y . - 2 - Question 2 (25 marks) (a) Ans: Produce 677.777771 units of super products X , no regular products X and 150 units of economy products X Maximum profit is $56833.33 X (b) Ans: [45–infinity, 45+21.66667]=[–infinity, 66.66667] Y (c) Ans: [300–149.444443, 300+infinity]=[150.555557, infinity] Y (d) Ans: Since the decrease in unit profit is $25 > 15 (allowable decrease) Y , the optimal solution and profit will be changed X . We need to revise and resolve the LP model X to obtain the new optimal solution and profit.
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