Branch banks must keep enough money on hand to satisfy customers$$ cash demands. Suppose that the daily demand for cash at a branch of University Bank follows a lognormal distribution with means and standard deviation summarized as follows $($in $$1,000$s$)$:

$$

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Mean

$$175$

$$120$

$$90$

$$60$

$$120$

$$140$

$$65$

Std Dev

$ $26$

$ $18$

$$13$

$ $9$

$ $18$

$ $21$

$ $9$

An armored truck delivers cash to this bank once a week. The manager of the bank can order any amount of cash she desires for this delivery. Of course, running out of cash in any week is very undesirable as customers of the bank expect to be able to withdraw their deposits on demand. Of course, keeping excessive cash reserves would guard against this happenstance. However, cash is a non$-$interest earning asset, so there is an opportunity cost for holding excess cash reserves.