Consider the following all-integer linear program:
Max 5x1 + 8x2
s.t.
6x1 + 5x2 ≤ 30
9x1 + 4x2 ≤ 36
1 x1 + 2 x2 ≤ 10
x1, x2 ≥ 0 and integer

a. Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.
b. Find the optimal solution to the LP Relaxation. Round down to find a feasible integer solution.
c. Find the optimal integer solution. Is it the same as the solution obtained in part (b) by rounding down?