4) Consider the following LP model and the corresponding feasible region. Minimize Z 50 x1 +...

  

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4) Consider the following LP model and the corresponding feasible region. Minimize Z 50 x1 + 50 x2 s.t. 3 x1 + 2 x2 150 (Constraint 1) 2 x1 + 3 x2 120 (Constraint 2) 3 x1 + 2 x2 XI - X2 VI NI < 180 (Constraint 3) 0 (Constraint 4) X1, X2 > 0 (Non-negativity constraints) x2 (3) (2) (4) (1) Feasible Region x1 Given that the optimal solution is: x*= (42,12) and Z*=2700: (a) Find the minimum value that the coefficient of x1 in the objective function can take so that the optimal solution (the optimal values of x1 and x2) does not change? (b) How will the optimal solution change if the objective function is changed as: "Maximize 50 x1 +50 x2"? Explain. (c) Suppose that the sign of Constraint (1) is changed to "". Does the feasible region change? Does the optimal solution change? If so, determine the new feasible region, the optimal solution and the value of Z. 4) Consider the following LP model and the corresponding feasible region. Minimize Z 50 x1 + 50 x2 s.t. 3 x1 + 2 x2 150 (Constraint 1) 2 x1 + 3 x2 120 (Constraint 2) 3 x1 + 2 x2 XI - X2 VI NI < 180 (Constraint 3) 0 (Constraint 4) X1, X2 > 0 (Non-negativity constraints) x2 (3) (2) (4) (1) Feasible Region x1 Given that the optimal solution is: x*= (42,12) and Z*=2700: (a) Find the minimum value that the coefficient of x1 in the objective function can take so that the optimal solution (the optimal values of x1 and x2) does not change? (b) How will the optimal solution change if the objective function is changed as: "Maximize 50 x1 +50 x2"? Explain. (c) Suppose that the sign of Constraint (1) is changed to "". Does the feasible region change? Does the optimal solution change? If so, determine the new feasible region, the optimal solution and the value of Z.