Part $1$: $[10$ marks$]$

Given the following gasoline data:

Compute the seasonal index for each quarter.

$[6]($show detailed calculations$).$

Suppose we expect year $2000$ to have annual demand of $800.$ 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 $60$ dozen cases of eggs a day that they order from an egg

factory with a lead time of five days. One fine day they stock their chiller and note

that there are only $25$ dozen cases of eggs remaining. They have a backorder of $15$

cases and an open order of $200$ cases.

What is their inventory position?

Should they place an order?

note: show detailed calculations