2. You are provided with the following integer program:

max z = x + 2y

s.t.

5x + 2y 30

4x y 3

y 3.5

x, y 0 and integer

(a) On the following page, use the graphical solution method to identify the feasible points. Use the scale 1 by 1 for each small square in the graph.

(b) Find the extreme points of the LP relaxations feasible region. Extreme point 1: Extreme point 2: Extreme point 3: Extreme point 4:

(c) Find the extreme points of the convex hull and calculate their objective values.

(d) Draw an isoprofit line that passes through the point (x = 4, y = 0) and find the direction of optimization.

(e) Provide the optimal solution and optimal objective function value.

Optimal solution: x = _______ y = _________

Optimal objective value:______________