This paper presents a novel mixed integer linear programing (MILP) formulation for finding the optimal layout of a fixed number of identical turbines that maximizes wind farm power generation. Previous MILP formulations with power maximizing objectives discretize the feasible space by using a grid of possible turbine locations. The proposed MILP formulation takes a different approach by allowing unrestricted placement of turbines, but treats wake cone overlap as a binary outcome. The rationale behind the proposed formulation is that the expansion of the feasible space for turbine placement in the proposed formulation would offset the disadvantage of using a lower fidelity binary wake cone overlap model. For small wind farms, the proposed formulation was able to produce superior layouts compared to a grid-based MILP formulation.