Problem 3 (20 Marks) Use Graphical Method as discussed in class to solve two-variable linear programming (LP) problems. 1) Solve the following LP problem Maximize Z(X1, X2) = 3x1 + 2x2 Subject to 2x1 + x2 0 1.1) Draw the graph corresponding to the given constraint inequalities and non-negative conditions based on the above LP model. 1.2) On your graph, clearly identify the region of feasible solutions (feasible region) of this LP model. 1.3) On your graph, use a dashed line to demonstrate how the optimal solution of this problem is to be found. 1.4) Identify from your graph or calculate the value of the optimal solution (xi,x;). 1.5) Calculate the corresponding optimal objective function value Z(xi,x;). 2) Solve the following LP problem. Note that in this LP problem, the constraint functions are the same as in 1) above and the objective function Z is different. Maximize 2(x1,x2) = 4x + 2x2 Subject to 2x1 + x2