See the pic below.

Consider a transportation problem with two source nodes 31,52, and n demand nodes 1, . . . ,n. All arcs (31-, j) are assumed to be present and to have innite capacity. Let D = 22:1 di be the total demand. Let the supply at each source node be equal to D/ 2. Assume that di > 0 for all i. (a) (4 points) How many basic variables are there in a basic feasible solution? (b) (6 points) Show that there exists a degenerate basic feasible solution if and only if there exists some set S C {1, . . . ,n} such that Eras di = D/2