Consider the following IP problem: Maximum Z= 5x1+x2

subject to
-x1+2x2 <=4
x1-x2 <=4
4x1+ x2 <=12

and
x1 >=0, x2>=0
x1, x2 are integers

a. Solve this problem graphically.
b. Solve the LP relaxation graphically. Round this solution to the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding the solution for the LP relaxation in all possible ways (i. e., by rounding each noninteger value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate Z. Are any of these feasible rounded solutions optimal for the IP problem?