Problem $2.(20$ points$)$

Excelsior Springs Ltd$.$ schedules production of one end product, Hi$-$Sulphur, in batches of $80$ units whenever the projected ending inventory balance in a quarter falls below $10$ units. It takes one quarter to make a batch of $80$ units. Excelsior currently has $30$ units on hand. The sales forecast for the next four quarters is:

Quarter

$1$

$2$

$3$

$4$

Forecast

$20$

$70$

$70$

$20$

a$.$ Prepare a time$-$phased MPS record showing the sales forecast and MPS for Hi$-$Sulphur.

b$.$ What are the inventory balances at the end of each quarter?

c$.$ During the first quarter, no units were sold. The revised forecast for the rest of the year is:

Quarter

$2$

$3$

$4$

Forecast

$30$

$50$

$70$

How does the MPS change?