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Graph the constraints determine the feasible set and use

Question: Consider the following linear programming problem

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(a) Graph the constraints, determine the feasible set, and use the graphical solution method to determine the optimal solution point. Which constraints are binding at optimum? Compute the exact coordinates at optimum and calculate the value of the objective function at optimum.

(b) What if the objective were Min z = - 3x1 - x2? Plot the new objective, use the graphical solution method, determine the optimal solution point, its coordinates, and the value of the objective function at optimum.

(c) Repeat (b) with the objective function Min z = x1 - 2x2.

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