$($Prob$.2)$ Quick Loan offers customized loans. Consumers call a toll$-$free number with a specific loan request and obtain a response within an hour. Quick Loan$$s business process includes five activities that must be conducted in the sequence described below. Three workers perform the whole process in a worker$-$paced line. The assignment of tasks to workers is the following: Worker $1($activity $1),$ Worker $2($activities $2$ and $3),$ and Worker $3($activities $4$ and $5).$ Each worker is paid $$20$ per hour. Assume that there is unlimited demand and that loans are entering at the bottleneck rate.

$($Activity $1)$ Answer customer calls and records key information $(4$ minutes$/$loan$)$

$($Activity $2)$ Gather and format the information $($e$.$g$.,$ obtain credit scores, organize customer$-$specific needs$)$ for analysis $(5$ minutes$/$loan$)$

$($Activity $3)$ Analyze the information: Check the creditworthiness and decide the loan amount and APR to offer $(7$ minutes$/$loan$)$

$($Activity $4)$ Perform final checks on the loan offer $(2$ minutes$/$loan$)$

$($Activity $5)$ Call the customer back with the new loan offer and close $(4$ minutes$/$loan$)$

$($a$)$ What is the bottleneck in the process?

$($b$)$ What is the maximum number of loans the company can process per hour?

$($c$)$ What is the labor cost per loan?

$($d$)$ What processing time is required to process $10$ loans per hour?