Editing The NEM Problem (section)

=Solving=
To solve the problem it soon becomes clear, that all locations and the amounts of ingredients in the bags and in storage need to be taken into account. To simplify the math it is also advisable to calculate in a common unit, which is in this case emu. We do not want to intruduce numbers too soon but work with variables to make it work for a wide application. For the conversion we introduce a matrix '''Y''', which we will use in the end to reverse the process and return to the number of items. While analysing the problem, it seemed logical to generate a seperate Transport Matrix for each way. The numbers "-1" and "1" mean to take or to put something from and in a bag respectively. <br />
As a thought experiment one can imagine that there are two mules with identical mule capacity and same path length and same speed starting from opposite bags. This progress we will define as one turn. '''e''','''f''','''g''' and '''M''' (for Mule Capacity is a scalar) will remain variables. Matrix '''T''' is used to balance the ingredients in each bag. We regard the transport as finished and look at the bags again to calculate how many more iron ore and coal need to be harvested in each place. It is important to note that the number of foreign ingredients do not change at this point anymore. This is only in theory. For practical use, harvesting and transporting ingredients can happen at the same time. At last we want to introduce a vector '''N''' which contains the multiplictors for the ingredients for the final product. Please read paper from 11.06.15 [https://drive.google.com/file/d/0BzdNczFxfj7wS0hGX2k3MWl5Nnc/view NEMv2.pdf] <br />

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[[File:NEMeq.jpg|thumb|600px|center|Preview NEM equations]]