$12.$ To facilitate operations on a highway system, a logistics company is seeking to minimize the costs of transporting imported products from two seaports to three cities inland. Assume that at each source, there is no excess, that is$,$ every material that needs to be shipped is shipped. The quantity of products generated at the source nodes, the capacities of the destination nodes, the node$-$to$-$node link distances $($miles$),$ and the transport costs $($S mile$)$ are provided in Table $17\mathrm{.}13.$ How much material must be transported from each source to each destination?