Suppose you had a system which has two subsystems in series. Further, subsystem A is composed on three identical components, Ai$,$ with two components in cold standby. Subsystem B is composed of two identical components, Bi$,$ in hot standby. The system can be depicted as$,$

If the MTBF for each component in subsystem A is $30$ hours, and the MTBF for each component in subsystem B is $45$ hours, then what is the total MTBF for the system?

Answer choices:

$28\mathrm{.}8$ hours

$35\mathrm{.}5$ hours

$42\mathrm{.}8$ hours

$38\mathrm{.}6$ hours