Based on Sonderman and Abrahamson (1985). In treating a brain tumor with radiation, physicians want the maximum amount of radiation possible to bombard the tissue containing the tumors. The constraint is, however, that there is a maximum amount of radiation that normal tissue can handle without suffering tissue damage. Physicians must therefore decide how to aim the radiation to maximize the radiation that hits the tumor tissue subject to the constraint of not damaging the normal tissue. As a simple example of this situation, suppose six types of radiation beams (beams differ in where they are aimed and their intensity) can be aimed at a tumor. The region containing the tumor has been divided into six regions: three regions contain tumors and three contain normal tissue. The amount of radiation delivered to each region by each type of beam is shown in the Sonderman and Abrahamson spreadsheet. If each region of normal tissue can handle at most 60 units of radiation, which beams should be used to maximize the total amount of radiation received by the tumors? MaxUnits Tot Dlvd Unitsblvd Used -Model I$E$29 Modell$B$23:$D$23 Modeli$$ 14:$B$19 SE BO OWN Normal 3 12 9 20 18 17 Tumor 1 30 27 20 9 20 15 Tumor 2 18 23 15 27 Tumor 3 9 12 26 24 21 15 . 8 11 15 2 3 Data 4 Beam Normal 1 Normal 2 1 24 18 2 18 15 3 14 12 4 6 18 5 14 6 10 6 12 11 11 12 Beams used 13 Beam Used 14 1 15 2 16 3 17 4 18 5 19 6 20 21 Constraints on normal tissues 22 Normal 1 Normal 2 23 Units delivered 24 25 Maximum 60 60 26 27 Units delivered to tumors 28 Tumor1 Tumor 2 29 30 31 32 33 34 35 36 37 Sunblessed Juice Company Normal 3 60 Tumor Total NASA Sonderman and Abrahason Extra Credit +