Suppose we have a flow network, with capacity constraints on _weighted sums_ of arc flows, such as:

2 * f(1, 2) + 3 * f(4, 5) + f(3, 7) <= 10,

where f(1, 2) denotes the flow through arc (1, 2).

Can the problem of computing a maximum flow (or min-cost max flow) for these networks be reduced in a straightforward way to a problem where we have a capacity constraint per arc?

I've found a similar but unanswered question from 2012 [here](http://mathoverflow.net/q/97841/67129), and Google pointed me towards some articles on _shared flow_, but this problem seems to be slightly different. Also, parametric max flow seems related, but I don't see how it matches this problem.