Conduct a Miller$-$Orr analysis using the data in problems $6$ but with a lower cash limit of $$5,000.$

a$.$ What should the cash return level be$,$ using the Miller$-$Orr model?

b$.$ What is your estimate of the average cash balance if the Miller$-$Orr calculation is used to set the cash return level?

c$.$ How do you explain your finding in part a to the assistant treasurer, who wants to know how to use the information provided by the model?

d$.$ If the variance of daily net cash flows is $$10,000,000$ instead of $$5,000,000,$ how does this change the answer determined in part a$?$ Is the cash return level double your earlier result? How do you interpret this?