ToysInc.

SKU

Mean demand $($units$/$month$)$

Std$.$ Deviation $($units$/$month$)$

Unit cost $($$$/$unit$)$

Unit Sale Price $($$$/$unit$)$

Optimus Prime

$15000$

$2000$

$$16$

$$20$

Bumblebee

$10000$

$3000$

$$20$

$$23$

Starscream

$10000$

$1500$

$$14$

$$16$

For the data provided for ToysInc, suppose the holding cost per unit per month is $3\%$ of the cost of the item, and the backorder cost is $20\%$ of the profit margin per month. The lead time to replenish the toys from the manufacturer in South Eastern China is two months. The fixed cost of an order is $$500$ for any toy order.

The average inventory for Optimus Prime will be: