An administrator of a computer network asked his employer to purchase a new computer with an improved sound system. He wants to transfer his data collection from an old computer to the new one using a local network as shown below, where node O denotes the old computer and N denotes the new computer.

The numbers labeled on each data link (edge) specify the maximum transfer rate of that link. We assume that each link can transfer data in either direction, but not in both directions simultaneously. For example, through the link (A, B), one can either send data from A to B at any rate from 0 to 1, or send data from B to A at any rate from 0 to 1. Moreover, all data entering nodes A, B,.., E has to be sent further immediately, which indicates that the maximum transfer rate cannot be used on all links simultaneously (consider node A for an example). Therefore, we have to find an appropriate value of the data flow for each link so that the total transfer rate from O to N is maximum. Please transform this problem into a linear programming problem