Time left $0$:$56$:$34$

Question $13$

Not yet answered

Points out of $10\mathrm{.}00$

Remove flag

Question text

A small grocery store has a single checkout line. On a typical day customers arrive at the checkout on an average of one every $8$ minutes $($lets assume exponential interarrival times$).$ The cashier takes an average of $6$ minutes $($lets also assume the service time has exponential distribution$)$ to process a single customer. We assume that the service time is randomly distributed, and the customers arrive randomly. The store's owner believes that the amount of time that a customer has to wait hurts his business; he estimates that waiting time costs him $$20$ per customer$-$hour in lost business $($i$.$e$.$ Let's say $3$ customers wait for one hour, the store incurs a cost of $$20*3*1=$ $$60).$ In order to speed up service, the owner is considering hiring a teenager to bag the groceries at $$6$ per hour. With the addition of the bagger, the cashier will be able to process a customer in an average of $4\mathrm{.}5$ minutes. What is the wait time cost in no$-$bagger and with$-$bagger scenarios. Should the bagger be hired?