Xiaohei designed the system above with her engineering team.

$($a$)$ The overall system reliability is $64\mathrm{.}68\%($enter your response as a percentage rounded to two decimal places$).$

$($b$)$ If they have to pay $$4,200$ to fix a failed system, what is the expected failure cost of the system? $$1483($round your

response to the nearest dollar$).$

$($c$)$ If Xiaohei installs R$5$ as a backup for R$4.$ R$5$ has a reliability of $95\%.$ The probability of failure of the system with R$5$

is $10\mathrm{.}22\%($enter your response as a percentage rounded to two decimal places$).$

$($d$)$ How much should they pay for R$5$ at the maximum? $$1054($round your response to the nearest dollar$).$Please show work!