Three workstations are located on the circular conveyor of a manufacturing facility. Most of the flow between them moves from one station to the next on the conveyor. However, 7 units per minute must move from each station to the station after the next. As much as possible of this 2-step flow should be carried within the 11 units per minute capacity of each link of the conveyor.

The rest will be transported manually.

(a) Formulate a linear program to determine an optimal way to carry the flows.

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

(c) Show that your LP can be represented as a multicommodity flow problem by sketching the corresponding digraph and labeling with costs, capacities, and net demands.

(d) Explain why your multicommodity model would give meaningless results if all flow were combined into a single commodity.

(e) The optimal solution in this problem is fractional. Explain how this is compatible with the network nature of your multicommodity flow model.