Question: Consider the following linear programming (LP) problem. (80 points) Maximize z = X1 + 2x2, Subject to 21 + 3x2 0, x2 > 0. (a)

Consider the following linear programming (LP)

Consider the following linear programming (LP) problem. (80 points) Maximize z = X1 + 2x2, Subject to 21 + 3x2 0, x2 > 0. (a) Use graphical method to find the optimal solution. (b) Determine the ranges for the coefficients of the objective function that will keep the optimal solution unchanged. That is, find the optimality ranges for c and ca in z = C1X1 + C2X2. For c and c2 in these ranges, the current optimum solution (the one one obtained in part (a)) remains unchanged. (c) Solve the linear programming problem using the simplex method in tabular form. (d) Find the dual problem of the given linear programming

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