Suppose that there are three suppliers S1, S2, and S3 in a distribution system that can supply 5, 5, and 6 units, respectively, of the company's good. The distribution system contains five demand centers, that require 2, 2, 4, 4, and 3 units each of the good. The transportation costs, in dollars per unit, are as follows:
D1 D2 D3 D4 D5
S1 2 1 2 3 3
S2 2 2 2 1 -1
S3 3 3 2 1 2
a) Compute an optimum shipping schedule. Is the optimal solution unique?
b) Find the range over which the cost of transportation from S1 to D3 can vary while maintaining the optimal basis solution in part (a).
c) To investigate the sensitivity of the solution to this problem, consider what happens if the amount supplied from any one supplier and the amount demanded by any one demand center were both increased. Is it possible for the total shipping costs to decrease by increasing the supply and the demand for any particular choice of supply and demand centers?
d) A landslide has occurred on the route from S2 to D5. If you bribe the state highway crew with $10, they will clear the slide. If not, the route will remain closed. Should you pay the bribe?