W $(3\mathrm{.}1)8.$ The Fagersta Steelworks currently is working two mines to obtain its iron ore. This iron ore is shipped to either of two storage facilities. When needed, it then is shipped on to the company's steel plant. The diagram below depicts this distribution network, where M$1$ and M$2$ are the two mines, S$1$ and S$2$ are the two storage facilities, and $P$ is the steel plant. The diagram also shows the monthly amounts produced at the mines and needed at the plant, as well as the shipping cost and the maximum amount that can be shipped per month through each shipping lane.

Management now wants to determine the most economical plan for shipping the iron ore from the mines through the distribution network to the steel nlant.