Consider the following mixed-integer linear program:
Max 2x1 + 3x2
s.t.
4x1 + 9x2 ≤ 36
7x1 + 5x2 ≤ 35
x1, x2 ≥ 0 and x1 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 x1 down to find a feasible mixed-integer solution. Is this solution optimal? Why or why not?
c. Find the optimal solution for the mixed-integer linear program.