Question 1 (30 points) Consider the following linear optimization problem: Minimize Z= 3x + 4y S.T. (1) 3x + 2y > 1200 (2) x + 2y = 800 (3) x > 2y (4) x, y > 0 (a) Construct a rough sketch to represent this problem graphically. On this diagram, draw the boundaries of the constraints, clearly labeling them by number, showing their respective directions of feasibility by arrow(s) and identify the feasible region by shading. (b) Determine the coordinates of the feasible extreme points. (c) Find the optimal solution (i.e. x, y and Z values) and compute the values of the slack/surplus variables pertaining to the major constraints at optimality. (d) What is the optimal solution if the objective function is changed to Minimize Z= x 3y? (e) Find the optimal solution if the objective function is changed to Maximize Z= 3x + 4y