The following depicts a network flow problem, with labels on nodes indicating net demand and those on arcs showing capacity.

For each of the following lists of possible nonbasic arcs, either compute the corresponding basic solution and indicate whether it is basic feasible, or apply principle 10.33 to demonstrate that the unlisted arcs do not form a basis of the implied flow balance constraints.

(a) (1, 2), (2, 1), (3, 4), (5, 4) lower-bounded, (1, 3), (2, 5) upper-bounded

(b) (1, 2), (1, 4), (3, 4), (4, 5), (5, 4) lowerbounded, (1, 3), (3, 5) upper-bounded

(c) (1, 3), (2, 1), (2, 5), (3, 4), (5, 4) lowerbounded, (1, 4) upper-bounded

(d) (1, 2), (1, 4), (2, 3), (3, 4) lower-bounded, (2, 5) upper-bounded

(e) (1, 2), (1, 4), (4, 5) lower-bounded, (2, 5), (3, 4) upper-bounded

(f) (1, 2), (2, 1), (2, 5), (3, 4), (5, 4) lowerbounded, (1, 4) upper-bounded (g) (1, 2), (1, 4), (3, 4), (5, 4) lower-bounded, (1, 3), (2, 5), (3, 5) upper-bounded (h) (1, 2), (1, 4), (3, 4), (4, 5) lower-bounded, (1, 3), (2, 5) upper-bounded