This article proposes a bi-criteria formulation to find the optimal location of light rapid transit stations in a network where demand is elastic and budget is constrained. Our model is composed of two competing objective functions seeking to maximize the total ridership and minimize the total budget allocated. In this research, demand is formulated using the random utility maximization method with variables including access time and travel time. The transit station location problem of this study is formulated using mixed integer programming and we propose a heuristic solution algorithm to solve large-scale instances which is inspired by the problem context. The elastic demand is integrated with the optimization problem in an innovative way which facilitates the solution process. The performance of our model is evaluated on two test problems and we carry out its implementation on a real-world instance. Due to the special shape of the Pareto front function, significant practical policy implications, in particular budget allocation, are discussed to emphasize the fact that the trade-off between cost and benefit may result in large investments with little outcomes and vice versa.