Consider the following mixed-integer linear program:
Max 1x1 + 1x2
s.t.
7x1 + 9x2 ≤ 63
9x1 + 5x2 ≤ 45
3x1 + 1x2 ≤ 12
x1, x2 ≥ 0 and x2 integer
a. Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions.
b. Find the optimal solution to the LP Relaxation. Round the value of x2 down to find a feasible mixed-integer solution. Specify upper and lower bounds on the value of the optimal solution to the mixed-integer linear program.
c. Find the optimal solution to the mixed-integer linear program.