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**Final Exam** **Operations Research** **01/07/2016** 1\) The following is a payoff table giving profits for various situations. ------------------ ---------------------- ----- ----- **States of Nature** **Alternatives** A B C Altern...

**Final Exam** **Operations Research** **01/07/2016** 1\) The following is a payoff table giving profits for various situations. ------------------ ---------------------- ----- ----- **States of Nature** **Alternatives** A B C Alternative 1 200 170 100 Alternative 2 150 120 140 Alternative 3 240 110 105 ------------------ ---------------------- ----- ----- What decision would a pessimistic person make? A\) Alternative 1 B\) Alternative 2 C\) Alternative 3 D\) Alternative 1 or 2 E\) Alternatives 2 or 3 2\) The following is a payoff table giving profits for various situations. ------------------ ---------------------- ----- ----- **States of Nature** **Alternatives** A B C Alternative 1 200 170 100 Alternative 2 150 120 140 Alternative 3 240 110 105 ------------------ ---------------------- ----- ----- What decision would be made using regret criterion? A\) Alternative 1 B\) Alternative 2 C\) Alternative 3 D\) Alternative 1 or 2 E\) Alternatives 2 or 3 3\) The following is a payoff table giving profits for various situations. ------------------ ---------------------- ----- ----- **States of Nature** **Alternatives** A B C Alternative 1 200 170 100 Alternative 2 150 120 140 Alternative 3 240 110 105 ------------------ ---------------------- ----- ----- What decision would be made using criterion of realism (alpha = 0.4)? A\) Alternative 1 B\) Alternative 2 C\) Alternative 3 D\) Alternative 1 or 2 E\) Alternatives 2 or 3 4\) Consider the following linear programming problem: This is a special case of a linear programming problem in which A\) there is no feasible solution. B\) there is a redundant constraint. C\) there are multiple optimal solutions. D\) this cannot be solved graphically. E\) None of the above 5\) Consider the following linear programming problem: Maximize 15X + 20Y Subject to X + 2Y  140 2X + 3Y  300 1X + 2Y  100 X, Y  0 This is a special case of a linear programming problem in which \(a) there is no feasible solution. \(b) there is a redundant constraint. \(c) there are multiple optimal solutions. \(d) this cannot be solved graphically. \(e) none of the above 6\) Consider the initial simplex tableau below: Initial simplex tableau -M -M -M 0 0 0 30 40 20 → Cj Quantity (RHS) A3 A2 A1 S3 S2 S1 X3 X2 X1 Solution mix ↓ 90 0 0 1 0 0 0 -1 1 1 A1 -M 15 0 0 0 0 0 1 1 0 1 S1 0 50 0 1 0 0 -1 0 2 0 2 A2 -M 40 1 0 0 -1 0 0 -5 1 2 A3 -M Zj Cj - Zj Based on the initial tableau above, the fourth constraint is: A\) 2X~1~ + X~2~ -5X~3~ ≥ 40 B\) 2X~1~ + X~2~ -5X~3~ = 40 C\) 2X~1~ + X~2~ -X~3~ = 40 D\) 2X~1~ + X~2~ -5X~3~ ≤ 40 E\) None of the above 7\) Consider the initial simplex tableau below: Initial simplex tableau -M -M -M 0 0 0 30 40 20 → Cj Quantity (RHS) A3 A2 A1 S3 S2 S1 X3 X2 X1 Solution mix ↓ 90 0 0 1 0 0 0 -1 1 1 A1 -M 15 0 0 0 0 0 1 1 0 1 S1 0 50 0 1 0 0 -1 0 2 0 2 A2 -M 40 1 0 0 -1 0 0 -5 1 2 A3 -M Zj Cj - Zj Based on the initial tableau above, the first constraint is: A\) X~1~ + X~2~ -X~3~ ≥ 90 B\) X~1~ + X~2~ -X~3~ = 90 C\) X~1~ + X~2~ -X~3~ ≤ 90 D\) X1 + X2 -M ≥ 40 E\) None of the above 8\) Consider the initial simplex tableau below: Initial simplex tableau -M -M -M 0 0 0 30 40 20 → Cj Quantity (RHS) A3 A2 A1 S3 S2 S1 X3 X2 X1 Solution mix ↓ 90 0 0 1 0 0 0 -1 1 1 A1 -M 15 0 0 0 0 0 1 1 0 1 S1 0 50 0 1 0 0 -1 0 2 0 2 A2 -M 40 1 0 0 -1 0 0 -5 1 2 A3 -M Zj Cj - Zj Based on the initial tableau above, the pivot column is: A\) X~1~ B\) X~2~ C\) X~3~ D\) S~2~ E\) None of the above 9\) Consider the initial simplex tableau below: Initial simplex tableau -M -M -M 0 0 0 30 40 20 → Cj Quantity (RHS) A3 A2 A1 S3 S2 S1 X3 X2 X1 Solution mix ↓ 90 0 0 1 0 0 0 -1 1 1 A1 -M 15 0 0 0 0 0 1 1 0 1 S1 0 50 0 1 0 0 -1 0 2 0 2 A2 -M 40 1 0 0 -1 0 0 -5 1 2 A3 -M Zj Cj - Zj Based on the initial tableau above, the pivot number is: A\) -5 B\) 2 C\) 1 D\) 0 E\) None of the above 10\) If, in the final optimal simplex tableau, the Cj - Zj value for a basic variable is zero, this implies: A\) Infeasibility. B\) Unboundedness. C\) Degeneracy. D\) Alternate optimal solutions. E\) None of the above 11\) Consider the transportation table below: Transportation Table ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- **Supply** **Destination C** **Destination B** **Destination A** **From To** **300** 14 4 13 **Source 1** **140** 10 6 16 **Source 2** **100** 4 11 8 **Source 3** **220** **140** **180** **Demand** ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- Based on the transportation table above, total transportation cost using North-West Corner Method will be: A\) 4560 B\) 4550 C\) 4540 D\) 4200 E\) None of the above 12\) Consider the transportation table below: Transportation Table ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- **Supply** **Destination C** **Destination B** **Destination A** **From To** **300** 14 4 13 **Source 1** **140** 10 6 16 **Source 2** **100** 4 11 8 **Source 3** **220** **140** **180** **Demand** ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- Based on the transportation table above, improvement index for cell 1C using North-West Corner Method as an initial solution will be: A\) 11 B\) -1 C\) 1 D\) 6 E\) None of the above 13\) Consider the transportation table below: Transportation Table ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- **Supply** **Destination C** **Destination B** **Destination A** **From To** **300** 14 4 13 **Source 1** **140** 10 6 16 **Source 2** **100** 4 11 8 **Source 3** **220** **140** **180** **Demand** ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- Based on the transportation table above, improvement index for cell 3A using North-West Corner Method as an initial solution will be: A\) 11 B\) -1 C\) 1 D\) 6 E\) None of the above 14\) Consider the transportation table below: Transportation Table ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- **Supply** **Destination C** **Destination B** **Destination A** **From To** **300** 14 4 13 **Source 1** **140** 10 6 16 **Source 2** **100** 4 11 8 **Source 3** **220** **140** **180** **Demand** ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- Based on the transportation table above, improvement index for cell 2B after getting first improved solution using stepping stone method will be: A\) 1 B\) -1 C\) 2 D\) 5 E\) None of the above 15\) Consider the transportation table below: Transportation Table ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- **Supply** **Destination C** **Destination B** **Destination A** **From To** **300** 14 4 13 **Source 1** **140** 10 6 16 **Source 2** **100** 4 11 8 **Source 3** **220** **140** **180** **Demand** ------------ ------------------- ------------------- ------------------- ------------- ---- -- -------------- Based on the transportation table above, cell 2C after getting first improved solution using stepping stone method will be shipped the quantity of: A\) 120 B\) 140 C\) 160 D\) Zero E\) None of the abov