Problem 1. [26 points] Consider the system shown below. The reliability of each process is listed at the top of the box. Components A and B are attached separately. Component C comes in a container (E) and has a backup (D). Component F is a backup if E fails. A, B, and E (or F) have to working order for the system to work. Please round all percentages to 4 decimal places. (a) [8 points] What is the reliability of the system? (b) [6 points] If $900 must be spent to fix a failed system, what is the expected failure cost of the system? Please round to the nearest dollar. (c) [12 points] If an 80% reliable backup for component A could be included at a cost of $45, should it be included in the product? Why or why not?
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