(c) Is (4, 1, 2) within the convex 2. Consider the following integer program (IP): max 5x+4x2 s.t. x1+x26 x1-2x22 10x16x245 X1, X2 Z (a) Solve the linear programming relaxation graphically. Let the optimal solution be XLP. (b) Let U, D and S be the vectors obtained when XLP is rounded UP, DOWN, and SCIENTIFICALLY, respectively. Are any of these vectors feasible for the original integer program? Without doing any additional analysis or work, can you determine if any of these vectors are optimal for the original integer program? Explain. (c) Solve the original integer program using exhaustive enumeration. Is the optimal solution any of your rounded solutions? 3. Continuation of Problem 2. (a) Outline the convex hull of the feasible region for the integer linear program (ILP). (b) What are the extreme points of the convex hull of the feasible region for the ILP? (c) Describe the convex hull of the original ILP using a system of linear algebraic inequalities.