Question $2$

A local major building contractor will utilize a total of $80,000$ bags of sand for completing a

new private commercial building project with a contract period of $4$ years. In order to make

each order of sand, it will take one third of an hour of a purchasing staff at $$66$ per hour of

wages, half of an hour of a technician with the salary of $$36$ per hour, and $$10$ for materials,

phone and mailing charges. The holding cost per average stock per year is $$8.$ It is also

assumed that the total working days for the project is $250$ days per year, and the lead time

between the placement of a new order and the receipt of the order is $3$ working days.

$($a$)$ On behalf of the contractor, recommend the best re$-$order policy based on the above

information and data by determining the: $($i$)$ optimal order quantity per order; $($ii$)$

annual ordering cost; $($iii$)$ annual holding cost; $($iv$)$ total annual inventory cost; $($v$)$

optimal number of orders that should be placed per year; and $($vi$)$ re$-$order point

$($ROP$).$

$($b$)$ If the optimal order quantity is changed to $400$ bags, what would be the $($i$)$ ordering

cost for each order; and $($ii$)$ holding cost per bag per year, under the optimal order

policy?

$(6\%)$