The effective application of continuous gas lift entails solving the combinatorial optimization problem of optimally allocating limited resources. This work proposes a mixed integer linear formulation for the problem of maximizing oil field profit under multiple facility constraints such as limited lift gas, fluid handling, and storage capacities. Families of valid inequalities are identified and introduced into the basic model to render a stronger formulation. Numerical experiments using commercial and non-commercial software, and comparisons with published results, show that the proposed method yields fast solution with significant average increase in oil production rate and profit.