obtained in part $($c$)?$

$2.$ A supermarket is trying to decide how many cash registers to keep open. Suppose an average of $15$ customers arrive each hour, and the average checkout time for a customer is $3$ minutes. Interarrival times and service times are exponential. It costs $$20$ per hour to operate a cash register, and a cost of $$0\mathrm{.}25$ is assessed for each minute the customer spends in the cash register area. How many cash registers should the store open? $(20$ points$)$

Operation research $2$