Question #1: Solve the following problems. 1. A linear programming problem is given as follows: Maximize Z = X1 + 2x2 Subject to 3x1 + 2x2 > 18 2x + 3x2 = 36 x1 =12 X259 x1,x220 Solve the given problem by drawing a graph that contains the following: Lines for all the constraints Feasible solution area (shade the area) All the extreme points circled Variable values (decision, slack and surplus variables) at each extreme point next to the circle. For example, (X1, X2,S1, S2, ...) = (6,8,16,0,...). A line for the objective function with the exact slope over the optimal point 2. Choose all the possible changes which make Problem 1 have multiple optimal solutions. a) Addition of a new constraint, 4x1 + 8x2 18 2x + 3x2 = 36 x1 =12 X259 x1,x220 Solve the given problem by drawing a graph that contains the following: Lines for all the constraints Feasible solution area (shade the area) All the extreme points circled Variable values (decision, slack and surplus variables) at each extreme point next to the circle. For example, (X1, X2,S1, S2, ...) = (6,8,16,0,...). A line for the objective function with the exact slope over the optimal point 2. Choose all the possible changes which make Problem 1 have multiple optimal solutions. a) Addition of a new constraint, 4x1 + 8x2