Consider the LPP of maximizing 3x1 + 6x2 + x3 subject to the constraints x1 + 2x2 + 3x3 ≤ 6, x ≥0, x2 ≥0, and 1 ≥ x3 ≥ 0. (a) Graph the feasible set in R³. (b) Using the canonical form of this problem, find all basic feasible solutions (BFS). Hint: based on your graph from part (a), how many BFS are there? (c) Let A denote the vertex (0, 0, 0), B the vertex (6, 0, 0), and C the vertex (0, 3, 0) of the feasible set. Find all basic directions at each of these vertices/BFS. Hint: each of the vertices should have 3 basic directions. (d) For each of the basic directions you foud in part (c), find the corresponding reduced cost.