A space probe to be launched by NASA will contain a module of three scientific experiments. Because of the high cost of the launch vehicle and the probe and the importance of the experiments, there will be redundant experimental packages within the module. Environmental stress testing has resulted in a (non redundant) reliability estimate over the duration of the mission of 0.85, 0.90, and 0.95 for the respective experiments. There is a weight limitation of 350 pounds allocated to the module. How many redundant experiments of each type should be included in the module if their respective weights are 40, 30, and 50 pounds? Since a minimum of one unit of each experiment is required, 120 pounds of the 350 pounds allocated are already accounted for. The objective is to maximize the overall reliability of the module.

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