Question: QI) consider the following linear problem and its optimal solution to answer each of the following questions (Show and justify each answer of your work)

QI) consider the following linear problem and its optimal solution to answer each of the following questions (Show and justify each answer of your work) Max z=4 X1 +1 X2 S.t 1 X1 + 1 X2=6 ... (1) IX =5....(2) 1X2 Optimal solution Basic z (max) x2 x 1 sx5 X1 0.00 0.00 1.00 0.00 X2 0.00 1.00 0.00 0.00 SX3 1.00 1.00 0.00 -1.00 SX4 3.00 -1.00 1.00 100 $35 0.00 0.00 0.00 1.00 Solution 21.00 1.00 5.00 3.00 1) What is the shadow price for constraint (2) (2 Pts) 2) What is the range of this shadow price that keep the solution feasible? (5 Pts) 3) What will be the optimal solution of the problem (the value of z and all other variables) if the decision maker decide to increase constraint 2 by 3. (3 Pts) 4) What is the dual problem for this problem? (7 Pts) 5) What is the optimal solution for the dual problem? (3 Pts)

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