The multibeam technique, which enables antenna arrays to produce several beams or lobes in different directions, has been proposed to enable integrated sensing and communication for the upcoming sixth-generation of mobile communication systems. In this work, while adopting the multibeam technique, we optimize the power distribution between communication and sensing beams. Imposing constraints on the communication to ensure a minimum performance level, we look for the power control coefficient value that optimizes one of three suitable objective functions for sensing: the sensing signal-to-interference-plus-noise ratio, the Cramér-Rao lower bound of the angle-of-arrival estimator, and the mutual information between the sensing channel and the echo signals from the targets. We find that multibeam modeling leads to convex optimization problems, which are therefore suitable for real-time implementation. Our scheme manages the inherent trade-off involved in balancing the power between communication and sensing by using the optimum power coefficient. The numerical results show an improvement of the beam shape and the relevant performance metrics compared with the radiation pattern obtained by previously proposed multibeam schemes.