Maine Miracle’s 2 restaurants sell lobsters obtained from 3 fisherman. A total of 350 lobsters per day are served at the first restaurant, and 275 at the second. Each fisherman can ship up to 300 per day, but not all arrive suitable for serving. The following table show the cost

(including shipping) and the yield of servable lobsters for each combination of fisherman and restaurant.

Fisherman Restaurant Cost Yield (%)

1 2 1 2 1 $7 $7 70 60 2 8 8 80 80 3 5 5 60 70 Maine Miracle seeks a minimum total cost way to meet its restaurant needs.

(a) Formulate a linear program to determine an optimal plan.

(b) Use class optimization software to compute an optimal solution to your LP.

(c) Show that your LP can be represented as a minimum cost flow model with gains or losses by sketching the corresponding digraph and labeling as in Example 10.30.

(d) The optimal solution in this problem is fractional. Explain how this is compatible with the network nature of your flow with gains or losses model.