Butterfly, Inc. is making a $6-$month plan for the workforce levels at their plant in Indiana.

This plant produces two different excavators: XC$1$ and XC$2.$ The demand for each model

over the next six months is shows below.

It takes $5$ worker days to produce on XC$1$ and $8$ worker days to produce one XC$2.$ Each

worker will work for $20$ days per months. The initial inventory levels are expected to be $20$

units of XC$1$ and $40$ units of XC$2.$ Butterfly wants to have $30$ units of $xC1$ and $60$ units of

$xC2$ at the end of month $6.$

$($a$)$ Find the aggregate demand $($measured in worker days$)$ for each of the next six months.

$($The aggregate demand should reflect the desired ending inventory levels.$)$

$($b$)$ Butterfly decided to use a mixed strategy to plan the workforce levels. They will follow a

constant workforce plan in the first three months, and they will switch to a zero inventory

plan for the last three months. Find appropriate workforce schedule for months $1$ through

$3,$ month $4,$ month $5,$ and month $6.$

$($c$)$ At the end of month $6,$ what is the actual $($i$.$e$.,$ true, physical$)$ ending inventory level,

measured in terms of workers days? $($The desired ending inventory should be included

in the consideration.$)$