Please answer A through D

consider a grocery store between the hours of $5$pm and $8$pm on a week night. suppose three checkout lanes are typically open, each checkout can handle customers with any number of items, and each checkout has a dedicated bagger. it has been observed that checking out $($including bagging$)$ takes a mean of $3$ minutes per customer and that this is approximately normally distributed with a standard deviated of $\mathrm{.}5$ minutes. the mean amount of time between customer arrival at the checkouts is $1$ minute and can be approximated by an exponential distribution. Although customers initially enter one specific line, they will move to a different line if it looks faster.

Hint: model the three lines as a single line $($or buffer$)$ that feeds all checkouts. you can assume that everyone that arrives at the checkout gets into the single line, regardless of its length; thus, no one is rejected from the process. $($so make sure you single line is large enough$)$

a$.$ Draw a process flow map for your three lane model.

For parts b and d$,$ perform $100$ simulations for each. Assume there is no one in line at the beginning of the simulations.

b$.$ Run the model from part and report for the single line, overall mean number of customers in line and the overall mean waiting line.

c$.$ How much would the overall mean numbers of customers in line and the overall mean waiting time in line be reduced by opening a fourth checkout?

d$.$ The owner of the grocery store chain is considering the purchase of new bar code scanners. This would reduce the mean checkout time to $2\mathrm{.}6$ minutes $($still normal$),$ with a standard deviation of $\mathrm{.}5$ minutes. For the three$-$lane case, what effect would this have on the overall mean number of customers in line and the overall mean waiting time in line?

Please explain how to do each step very thoroughly!