Radiotherapy is a usual cancer treatment that poses challenges in creating optimal treatment plans to balance cancer elimination and minimize side effects. Computer systems can assist by optimizing beam angles and exposure. This study focuses on intensity-modulated radiation therapy. We propose four linear and quadratic mathematical models to solve the Fluence Map Optimization problem and present an ad hoc heuristic for beam selection. The algorithm employs an iterative approach to solve linear programming models to select the most favorable beam at each iteration. Experimental assessment considered liver cancer instances. The algorithm found solutions that met all medical constraints for all cases tested.