#$1.$ Consider an EOQ model with safety stock; the optimal order quantity, EOQ is $585,$ and

safety stock $($SS$)$ is $63.$ What, on average, would be the "maximum inventory" observable on the

inventory$-$time graph, and what would be the average minimum inventory on that graph?

Calculate average inventory. $(12$ points$)$

$In{v}_{\text{m}\text{a}\text{x}}=$

$In{v}_{\text{m}\text{i}\text{n}}=$

AVERAGE inventory $=$

#$2.$ Customers arrive at a "check$-$out area" one every twenty$-$seconds and join "one of the

NINE customers' lines"; each line leads to ONE cashier. Each cashier takes on average $2\mathrm{.}5$

minutes to checkout a customer. $(3+6+11=20$ points$)$

$($i$)$ What is the name of this waiting line setup $($what model is in use$)?$

$($ii$)$ Suppose you are studying any ONE of these lines $($since they are statistically identical$),$

what would be the values of $$ and $$ that you will use?

$($iii$)$ Consider a store using a single channel model for its cashiers with a number of customer

lines; an operations analyst is studying the lines. There are SIX statistically identical lines so

he$/$she has to study only one line. He$/$she calculates $=\frac{20}{?}$ hour and $=\frac{25}{?}$ hour. What is

the average time a customer takes to checkout after joining a line? $(10$ points$)$