The demand for computational resources is steadily increasing in experimental high energy physics as the current collider experiments continue to accumulate huge amounts of data and physicists indulge in more complex and ambitious analysis strategies. This is especially true in the fields of hadron spectroscopy and flavour physics where the analyses often depend on complex multidimensional unbinned maximum-likelihood fits, with several dozens of free parameters, with an aim to study the internal structure of hadrons. Graphics processing units (GPUs) represent one of the most sophisticated and versatile parallel computing architectures that are becoming popular toolkits for high energy physicists to meet their computational demands. GooFit is an upcoming open-source tool interfacing ROOT/RooFit to the CUDA platform on NVIDIA GPUs that acts as a bridge between the MINUIT minimization algorithm and a parallel processor, allowing probability density functions to be estimated on multiple cores simultaneously. In this article, a full-fledged amplitude analysis framework developed using GooFit is tested for its speed and reliability. The four-dimensional fitter framework, one of the firsts of its kind to be built on GooFit, is geared towards the search for exotic tetraquark states in the [[EQUATION]] decays and can also be seamlessly adapted for other similar analyses. The GooFit fitter, running on GPUs, shows a remarkable improvement in the computing speed compared to a ROOT/RooFit implementation of the same analysis running on multi-core CPU clusters. Furthermore, it shows sensitivity to components with small contributions to the overall fit. It has the potential to be a powerful tool for sensitive and computationally intensive physics analyses.