Recall that in a flow network, the flow conservation property states that the sum of incoming flow to a node must equal the sum of outgoing flow from that node, except for the source and sink nodes.

Consider the standard form of a linear program (LP) where the objective is to maximize a linear function subject to linear equality and inequality constraints, and non-negativity conditions on the variables.

Formulate the maximum flow problem as an LP by defining variables for the flow on each edge, setting up constraints for flow conservation at each node (except source and sink), and adding capacity constraints for each edge. The objective should be to maximize the total flow out of the source (or into the sink).