6. A certain dosage of radiation, measured in kilorads, must be given to the tumor near the brain. The dose delivered must be sufficient to kill the malignant cells but the aggregate dose must not exceed established tolerance levels for the brain. Two beams which would deliver radiation exposure to the cells will be used. The goal is to select certain beam durations that would generate the best dosage distribution by minimizing the radiation absorbed by the brain. The data for the radiation therapy is given below: Fraction of dose absorbed per second Area Brain Spine Tumor Beam 1 0.4 0.3 0.5 0.6 Average dosage Beam 2 (in kilorads) 0.5 0.1 At most 2.7 0.5 At most 6 0.4 At least 6 Center of Tumor Determine the optimal exposure times for beam 1 and beam 2.