$2.(12$ pts$)$ An F$-35$ aircraft is estimated to fly $500$ hours a year. The aircraft MTBF is $125$ hours. Once an aircraft fails, the faulty component is isolated, removed and replaced with a spare, if available. $85\%$ of the time a spare is immediately available, and it takes $3$ days for fault isolation and component swap. If a spare is not available $(15\%$ of the time$),$ an aircraft is grounded for $18$ days $(3$ days for fault isolation and component swap, and $15$ days for waiting for a spare part$).$ The aircraft must go through depot overhaul maintenance every $5$ years which takes an average of $200$ days. The Navy$$s goal is to maintain $875$ FMC $($fully mission capable$)$ aircrafts in the F$-35$ fleet. How many F$-35$s does the Navy need in its inventory to meet this goal?