Suggest the following all-integer linear program: Max 5x1 +8x2 s.t. 6x1 + 5x2 <30, 9x1+4x2<36,1x1+2x2<10, x1,x2 > 0 and integer.
a. Graph constraints for this problem, employ dots to point out all feasible integer solutions.
b. Determine the optimal solution to the LP relaxation, round down to find out a feasible integer solution.
c. Determine the integer solution. Is it the same solution obtained in part (b) by rounding down?