Consider a two$-$stage process, with an infinite buffer between the two stages. The process starts at $7$ AM each day. The first stage operates $12$ hours a day and has three machines, each with a processing speed of $10$ gadgets$/$hour$.$ The second stage can operate continuously $(24/7)$ if necessary and has five machines, each with a processing speed of $4$ gadgets$/$hour$.$ Suppose the process starts empty at the beginning of each day. $($Choose the closest answer for the following questions$)$ What is the maximum inventory in the buffer during a day?

Group of answer choices

$48,$

$100,$

$120,$

$150$