Meta Kim is a mechanic at a workshop who can install new mufflers, averaging about one every 8 minutes, following an exponential distribution. Customers in need of this service arrive at the shop at an average rate of 7 per hour, following a Poisson distribution. The workshop owner would like to evaluate several options for its waiting line system. The cost of customer waiting time is $50 per hour of time spent waiting in line, reflecting customer dissatisfaction and lost goodwill. Kim is paid $30 per hour. The workshop owner has two other options available:

Option 1: Replacing Kim with an experienced mechanic who can efficiently install new mufflers in an average of 6.5 minutes each, but will be paid at a rate of $40 per hour.

Option 2: Opting for a new automated machine to install mufflers instead of hiring a mechanic. The machine can consistently install mufflers in 7.5 minutes per car. The cost of purchasing and operating the new machine will be amortized at a rate of $6 per car it serves.

Explain which option you will choose and why ? Justify your answer