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

$2$

$0$

$$days per months. The initial inventory levels are expected to be

$2$

$0$

units of XC

$1$

$$and

$4$

$0$

$$units of XC

$2$

$.$

$$Butterfly wants to have

$3$

$0$

$$units of

$$

$$

$1$

$$and

$6$

$0$

$$units of

$$

$$

$2$

$$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.

$)$

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