Question: Question No. 1( 10 Marks ) Consider the following Linear Programming Problem: Maximize 4X1 + 5X2 + 9x3 Subject to 1X1 + 1X2 + 1x3

Question No. 1( 10 Marks ) Consider the following

Question No. 1( 10 Marks ) Consider the following Linear Programming Problem: Maximize 4X1 + 5X2 + 9x3 Subject to 1X1 + 1X2 + 1x3 = 11 (Resource 1) 7X1 + 5x2 + 3x3 >= 62 (Resource 2) 3X1+ 5X2 + 10x3=0 While solving by Simplex Method we arrived at the following OPTIMAL Tableau: 5 j 4 X1 9 X3 -M A. M Az o Sz Co RHS X2 Sa 9 X3 0.50 { 1-75 -0.25 0.25 3.75 4 Xi 0.50 -0.75 0.25 -0.25 7.25 0 S3 o -1.50 - 45.25 1-75 -75 ! 29.75 zi 4 6.50 -1.25 1.25 62.75 12.75 -M -2.75 o o G-2; Lo -1.50 +25 -1.25 Answer the following questions: (a) Write down the DUAL problem associated with the above PRIMAL problem. (b) Write down the complete solution of the DUAL problem. (c) Compute the Ranges of Resource 1 within which the current OPTIMAL BASIS will NOT change, (d) What will be the new value of the objective function if one more unit of Resource 1 is added? (e) Compute the Ranges of profit associate with product X1 within which the current OPTIMAL BASIS will NOT change

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