Consider the following linear program. max subject to 4x + 2y x + y 3x + y x 9 18 5 y x/2 + y 6x + 7y -2 -9 a. Draw (by hand!) the feasible region of the above linear program. List all vertices of the feasible region with their (x, y) coordinates, and label the boundary lines of the feasible region with the corresponding inequalities of the linear program. b. What is the optimal solution for the linear program? State both the objective value of the optimal solution and its (x, y) coordinates. c. What is the optimal integral solution for the linear program? State both the objective value of this solution and its (x, y) coordinates. Is it the same or different as the optimal solution from part (b)?