a. Which constraints are active at the point (2, 0, 3)? b. Is the direction d=(-1, 1, -1) a feasible direction at (2, 0, 3)? c. Is the direction d = (-1, 1, -1) an improving direction at (2, 0, 3)? d. Could the point (2, 0, 3) be an optimal solution to the linear program? e. Is the point (2, 0, 3) a basic solution? Justify your answer. f. Is the point (2, 0, 3) an extreme point? Justify your answer. g. Is the point (2, 0, 3) degenerate?

Q9

9. In each part, determine whether the given 3-tuple is a solution of the linear system (a) (3, 1, 1) 2x1 - 4x₂ - x3 = X3 X₁ - 3x₂ + 3х1 — 5x2 — 3х3 (b) (3,-1, 1) x3 = = = (c) (13, 5, 2)

Consider the problemMaximize z = x1 + 5x2 + 3x3subject tox1 + 2x2 + x3 = 62x1 - x2 = 8x1, x2, x3 >= 0The variable x3 plays the role of a slack. Thus, no artificial variable is needed in the firstconstraint. In the second constraint, an artificial variable, R, is needed. Solve the problemusing x3 and R as the starting variables.