Methods and systems for performing well network production optimizations are described. For example, in one embodiment, a method of allocating an applied resource throughout a well network includes receiving topological data into an analytical model of a well network having one or more wells. The topological data includes a plurality of performance curves that relate well performance to one or more levels of an applied resource. The method also includes determining an optimum allocation of the applied resource using the analytical model to maximize an operating parameter of the well network, including converting a portion the analytical model having one or more wells and a linear inequality relationship to a modified portion having a single variable and a linear equality constraint.