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 2(x,x) = 3x + 2x2 Subject to 2x + xy S 12 -- *+ X2 S3 *y 2 0.x220 - 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. 13) On your graph, use a dashed line to demonstrate how the optimal solution of this problem is to be found. 1.4) Identity from your graph or calculate the value of the optimal solution (xi.x). 1.5) Calculate the corresponding optimal objective function value 26x1.x3). 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 z(x,x) = 4x1 + 2x2 Subject to 2x + xy S 12 - X1 + x2 53 4, 2 0.x2 > 0 2.1) On the solution graph, use a dashed line to demonstrate how the optimal solution is to be found. 2.2) Identify or calculate the value of one or more optimal solutions (x1 x3) at the corner(s) of the feasible region. 2.3) Calculate the corresponding optimal objective function value 2(xi.x3). 2.4) If you have found more than one corner optimal solution of this LP problem, indicate how many optimal solutions it has and indicate where these optimal solutions can be found