Consider the following IP problem.

Maximize Z 5x1 x2, subject to

x1 2x2  4 x1  x2  1 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 this 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?