Following is a maximizing, standard-form linear program and a classification of variables as basic and nonbasic.

x1 x2 x3 x4 max c 10 1 0 0 b

-1 1 4 21 13 2 6 0 -2 2 B N B B

(a) Compute the current basic solution.

(b) Compute all simplex directions available at the current basis.

(c) Verify that all your simplex directions are feasible at the current basic solution.

(d) Determine whether each of the simplex directions is improving.

(e) Regardless of whether it improves, determine the maximum step that preserves feasibility in each simplex direction and the new basis that would result after such a step.