How to maximize flow while satisfying lower bounds on flow through individual edges ?

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I was wondering if there is any way to solve the following problem:

" You are given a network graph. Every edge has two values associated with it: the upper bound of the amount of flow that CAN go through this edge and the lower bound of the amount of flow that MUST go through this edge. If there is no valid way to satisfy lower bound of all the edges, print "Unsolvable" . If there are multiple ways, maximize the amount of flow satisfying the lower bounds and upper bounds. You have to report the maximum amount only. "

No online judge has this problem ( at least none that I know of ). It's a random problem that came to my mind.
I know the algorithm to satisfy the lower bounds on edges in a network graph. But I am not sure about how to maximize flow while ensuring the lower bounds. I have a solution with the complexity of O(log(maxFlow) * complexity of finding maxFlow ) in mind. But I'm not entirely sure if it is right or wrong. I can discuss the idea in comments if anyone is interested.