This is a typical logistics model, with the corresponding network shown in the attached spreadsheet. Each net supplier’s net outflow cannot exceed the capacity shown in its node, each net demander’s net inflow must be at least the demand shown in its node, and each transshipment point must have a net outflow (and net inflow) of 0. The unit shipping costs are shown on the arcs, and the common arc capacity in the network is 1,200. The correct model and the optimal solution are shown in the attached spreadsheet.

Let the common arc capacity vary from 600 to 2,000 in increments of 100. Which of the following is true of the resulting optimal solutions?

a. For each of these common arc capacities, each supplier’s capacity constraint is binding except for supplier 1’s, and all demand constraints are binding.
b. When the common arc capacity is at least 1,600, the optimal total cost is the same as if there were no arc capacity constraints.
c. Even when the common arc capacity is 1,500 or less, there is at least one arc with flow equal to this capacity.
d. All of these choices are true.
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