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Problem 45-4 (Algo) A product engineer has developed the following equation for the cost of a system component: C = (10292, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of 3 identical components, all of which must operate for the system to operate. The engineer can spend $253 for the 3 components. What is the largest component probability that can be achieved? (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) Probability Problem 45-5 (Algo) The guidance system of a ship is controlled by a computer that has three major modules. In order for the computer to function properly, all three modules must function. Two of the modules have reliabilities of.86, and the other has a reliability of.98. a. What is the reliability of the computer? (Round your answer to 4 decimal places.) Reliability b. A backup computer identical to the one being used will be installed to improve overall reliability. Assuming the new computer automatically functions if the main one fails, determine the resulting reliability. (Round your intermediate calculations and final answer to 4 decimal places.) Reliability c. If the backup computer must be activated by a switch in the event that the first computer fails, and the switch has a reliability of .95, what is the overall reliability of the system? (Both the switch and the backup computer must function in order for the backup to take over.) (Round your intermediate calculations and final answer to 4 decimal places.) Reliability Problem 4S-7 (Algo) A production line has three machines A, B, and C, with reliabilities of.90,.95, and.92, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the lines reliability. Plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. In either case, three machines (A, B, and C) would be used with reliabilities equal to the original three. a. Compute overall system reliability under Plan 1. (Round your intermediate calculations and final answer to 4 decimal places.) Reliability b. Compute overall system reliability under Plan 2. (Round your intermediate calculations and final answer to 4 decimal places.) Reliability c. Which plan will provide the higher reliability? O Plan 1 O Plan 2