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Consider the problem of maximizing the revenuegenerated by tolls set on a subset of arcs of atransportation network, where origin-destinationflows (commodities) are assigned to shortest pathswith respect to the sum of tolls and initial costs.This work is concerned with a particular case of theabove problem, in which all toll arcs are connectedand constitute a path, as occurs on highways. As tolllevels are usually computed using the highwayentry-exit points, a complete toll subgraph isconsidered, where each toll arc corresponds to a tollsubpath. The problem is modelled as a linear mixedinteger program, and proved to be NP-hard. Severalclasses of valid inequalities are proposed, whichstrengthen important constraints of the initialmodel. Their efficiency is first shown theoretically,as these are facet defining for the restricted oneand two commodity problems. Numerical tests alsohighlight the practical efficiency of the validinequalities for the multi-commodity case. Finally,we point out the links between this problem and amore classical design and pricing problem in economics.