The standard simplex method is a well-known optimization algorithm for solving linear programming models in operations research. It is part of software often employed by businesses for solving scheduling or assignment problems. But their always increasing complexity and size drives the demand for more computational power. In the past few years, GPUs have gained a lot of popularity as they offer an opportunity to accelerate many algorithms. In this paper we present a mono and a multi-GPU implementation of the standard simplex method, which is based on CUDA. Measurements show that it outperforms the CLP solver on large enough problems. We also derive a performance model and establish its accurateness. To our knowledge, only the revised simplex method has so far been implemented on a GPU.