At a recent trade show, a French company unveiled its radical new prodact for the sports

equipenent industry $-$ a graphite hockey stick! The company, known as $"N$ lawee, $N$ Cowpone"

$($rough translation of $"$He Shooss, He Scores"$)$ has enthusiastic plans for the stick. As owners

of a medium$-$sized refial sporting goods store, you $($the student participants$)$ are keenly ware

of the various costs involved in ondering and holding imentory. Taking inte account the

respective coots, you are to develop an appropriate ondering policy for this brand$-$new item.

Since this is a new penduct, you have no historical dati on which to hase your forecast of

dennand. However, you are aware that hockey sticks are seasonal items. Hased on sales of

other winter sports equipment, you ohserve that sales follow three $4-$month "seasons". These

seasons are:

strong peak: September $-$ December $($inclusive$)$

weak peak: January $-$ Apnil $($inclasive$)$

slow: May $-$ Angest $($inclusive$)$

Your best bet as to demand during these periods is that it will follow a "unifonm" distribution,

with the following parameters:

strong peak: $40,70$

weak peak: $20,45$

slow: $5,25$

Consequently, the graphite hockey sticks demand during the month of September could fall

anywhere between $40$ and $70($any demand can occur with equal probability in that interval$).$

It will never be lower than $40,$ nor higher than $70.$ If it were the month of June, demand could

be anywhere between $5$ and $25($never lower than $5,$ never higher than $25).$

$"$N Lauce, A Coupse" will allow you to parchase hockey sticks for $$20.$ Market research

results given at the recent trade show indicated that potential customers woeld pay up to $$30$

for the item. Thus, you plan to use $$30$ as your selling price. Note that the amount you sell in

a given month is always the lowest of either monthly demand, or beginning imentory $-$

quantity ondered. Placing an order costs you $$60($note that the manufacturer allows at most

one replenishment per month$).$ Any unsatisfied dennand $($a stockout$)$ costs you $$7$ per unit

short in addition to the foregnne profit on this lost sale. Backonders are not allowed $($since

custoomers will most likely purchase the hockey stick: from a competion if you don't have

enough on$-$hand$).$ Inventory remaining at the end of a month costs you $$1$ per unit.

Your task is to plan replenishments $($when to onder, how much to onder$)$ on a month$-$by$-$month

hasis for the next $12$ months. Assume that the first moent in the planning horizon is July, and

that there is no iiventory on$-$hand. Afler you make your replemishment decision, the instructor

will announce the demand for that month. Then, you may make the decision for next month.

L$.$se the artached table io indicate your monthly replenishments, and to tabulate the results of

your respective strategy. If a stockout occurs, write $"0"$ for the ending inventory, and put a $"0"$

for the beginning inventory of the suhsequent month.