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    $\begingroup$ So it is a set of linear equations after all. This is exactly what I was looking for! Thank you so much =) $\endgroup$ Commented Sep 6 at 11:02
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    $\begingroup$ You're welcomeđź‘ŤYou put a great question together. $\endgroup$ Commented Sep 6 at 11:05
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    $\begingroup$ Hmm, I've been playing with it a little, and there seems to be either a misunderstanding on my side, or on your/code's side. If I decrease the amount of products two fold, making the amounts [3360, 1440, 1920, 2880], the result is four machines running at 100%, and two machines just sitting there doing nothing. This goes against the 3rd goal: "all of the available flow is equally distributed between each available machine, to the extent allowed within the specified constraints". The end result should be all machines running at 50% of their capacity instead. $\endgroup$ Commented Sep 6 at 17:17
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    $\begingroup$ You're right that the code tries to maximise utilisation. This is done by the minus sign at res = linprog(-unweighted_utilisation.ravel(), ...). If you remove the minus sign it will become a minimisation problem. I can see what you're saying - processing products as fast as possible implies minimising machine utilisation. $\endgroup$ Commented Sep 6 at 18:05
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    $\begingroup$ Yeah it feels like another constraint needs to be specified, or they need to be reconsidered. I ran the code and found utilisation is still maximal, even when minimising the objective. I will look into it. So you want maximal throughput, with at least 50% per machine? $\endgroup$ Commented Sep 6 at 18:18