It was $4$:$55$ on Friday afternoon before the NASCAR Sprint Cup

Series at Richmond International Raceway $($RIR$),$ a $3/4-$mile D$-$shaped

asphalt track that is known for its four $38-$foot by $24-$foot high$-$

definition LED screens used to broadcast live race action. Alex

Halek, Jefferson Plumbing Supplies' Inventory Manager, was looking

forward to spending the weekend at the race with two of his friends

whom he had not seen since last year's Sprint Cup. He returned to

his office to read a few letters that were waiting on his desk before

heading home to prepare for his annual rendezvous with his friends

on the track.

The first letter he opened was from Faucet Masters, a long$-$time

supplier of a specialty faucet. This was a unique faucet that did not

sell at a large volume but was steadily ordered by Jefferson's loyal

customers at the rate of $100$ units annually. The salespeople often

commented that having the faucet available in stock was crucial to

retaining some customers. The letter started with Faucet Masters

expressing its gratitude for the long$-$term business relationship with

Jefferson Plumbing. The letter also announced that lately the com$-$

pany had adopted a new minimum$-$order$-$size policy. Consequently,

faucet number $36543$ should be ordered at a minimum of $130$ units.

This new requirement caught Alex by a surprise as it was about three