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

$\backslash$table$[[$Quarter$,$Year $1997,\backslash$table$[[$Year$],[1998]],\backslash$table$[[$Year$],[1999]],\backslash$table$[[$Year$],[2000]]],[1,100,95,100,],[2,55,60,65,],[3,70,90,80,],[4,80,65,55,]]$

$1.$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 $2000?$

$[4]$

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?

$[3]$

Should they place an order?

$[2]$

note: show detailed calculations