Part $1$: Given the following gasoline data: $[10$ marks$]$

$1.$Compute the seasonal index for each quarter. $($Show detailed

calculations$).[6]$

$2.$Suppose we expect year $2000$ to have annual demand of $1600.$ What

is the forecast value for each quarter in year $2000?$

Part $2$: $[5$ marks$]$

Jimmy's Egg is a specialty restaurant featuring $47$ different kinds of

omelettes in three different sizes. They use $40$ dozen cases of eggs a day

that they order from an egg factory with a lead time of four days. One

fine day they stock their chiller and note that there are only $35$ dozen

cases of eggs remaining. They have a backorder of $25$ cases and an open

order of $200$ cases.

What is their inventory position?

Should they place an order?

$[2]$

note: show detailed calculations