Question: Consider the following LP problem: Minimize Z = 7x - 14y S.T. (1) x + y = 40 (2) y = (1/3)x (3) 3x +

Consider the following LP problem: Minimize Z =

Consider the following LP problem: Minimize Z = 7x - 14y S.T. (1) x + y = 40 (2) y = (1/3)x (3) 3x + 5y 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 clearly identify the feasible region. (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) If the objective function changes to Maximize Z = 5x + 2y, find the new optimal values of x, y, Z and all the slack and surplus variables

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