Cabot Appliances, a retail chain, is trying to decide what size order it should place

with its supplier of room air conditioners. Room air conditioner sales are highly sea$-$

sonal, and the number of units sold is very dependent on summer weather patterns.

Cabot places one order per year. Reorders are impractical after the selling season

begins to develop. Although the actual sales level cannot be known for sure, Cabot

analyzes past selling seasons, long$-$term weather reports, and the general state of the

economy. The following probabilities of various sales levels are then estimated:

A unit has a delivered price to Cabot of $$320$ and it is priced to customers at $$400.$

Air conditioners unsold at the end of the season are discounted to $$300,$ which

clears them from inventory. Purchases can be made only in increments of

$250$ units, with a $500-$unit minimum order.

a$.$ Assuming no inventory is to be carried to the next year, what single order

size should be placed?

b$.$ Would you modify the order quantity in part a if Cabot can borrow money to

support inventory at $20$ percent per year? Excess units can be carried over to

the next selling season.