Same Case as Above: Clifford Jones, the mechanic at Guns up Muffler is able to install $1$ new muffler every $20$ minutes according to a negative exponential distribution. Customers seeking this service arrive at the shop on the average of $2$ per hour, following a Poisson distribution. They are served on a first$-$in$,$ first$-$out basis and come from a very large $($almost infinite$)$ population of possible buyers.

The manager at Guns up Muffler, Audrey Jones, estimates that the cost of customer waiting time in terms of customer dissatisfaction and lost goodwill is $$15$ per hour waiting in line. Jones, the mechanic is paid $$11$ per hour and works $8$ hours per day.

However, funs up Muffler is going to buy new equipment that will cost $$10,000$ and will increase its service rate to $6$ cars per.

How much is this costing Guns up Muffler in customer dissatisfaction per day? And how many days until the equipment pays itself?

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$$20$ per day, $72$ days

b $$20$ per day, $104$ days

c $$160$ per day, $72$ days

d $$160$ per day, $104$ days