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Question 1: (40pts) Consider a LP problem as following Maximize Z=X1+5X2+3X3 Subject to: X1+ 2X2+X3=32X1X2=4X1,X2,X30 a) (15 points) Solve this problem by using Big M method or Two- phase method. b) (10 points) Find the range of values of X1 for which the current basis remains optimal. c) (5 points) Write the associated dual problem. d) (10 points) Determine the associated optimal dual solution..

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Question 1: (40pts) Consider a LP problem as following Maximize Z=X1+5X2+3X3 Subject to: X1+ 2X2+X3=32X1X2=4X1,X2,X30 a) (15 points) Solve this problem by using Big M method or Two- phase method. b) (10 points) Find the range of values of X1 for which the current basis remains optimal. c) (5 points) Write the associated dual problem. d) (10 points) Determine the associated optimal dual solution.

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