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 work in order for the system to work. Please round all percentages to 4 decimal places (e.g., 45.87%).

A = 90%

B = 84%

c =60%

D = 50%

E = c and D together

F = 40%

a. What is the reliability of the system?

b. If $900 must be spent to fix a failed system, what is the expected failure cost of the system? (Please round your answer to the nearest dollar.)

c. 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?