The bumper car section of an amusement park is a popular attraction that generates a significant

portion of the park$$s revenue. However, from time to time, cars break down and need to be repaired.

This not only affects the park$$s reputation but also leads to a loss of revenue as customers are unable

to use the attraction. The manager of the amusement park is faced with the task of hiring a repair

team to fix the broken cars.

The average number of cars that break down in the bumper car section is $2$ every hour. The

loss of revenue due to a breakdown of each car is $$40$ per hour. The manager can choose from two

types of repairmans to hire: For the first type of repairman, the average repair time of each car is

$20$ minutes, and for the second type, it is $15$ minutes. Hiring the first type repairman costs $$40$ per

hour, but hiring the second type$$s cost is $$60$ per hour as the repairmans of this type have higher

expertise and can finish repairing each car faster. Considering the above information, answer the

following questions: