Question $15$: Store A$\text{'}$s Average Inventory Level

To find the average inventory level, we can use the Economic Order Quantity $($EOQ$)$ model. The EOQ formula is given by:

Where:

$-$

is the demand $($in units$),$

$-$

is the setup $($ordering$)$ cost per order, and

$-$

is the holding cost per unit per year.

In this case:

$-$

bags of fertilizer per year,

$-$

$($ordering cost per order$),$

$-$

$($holding cost per unit per year$).$

First, calculate the EOQ:

So$,$ the EOQ is approximately $89\mathrm{.}44$ cases. Since Store A$\text{'}$s order quantity is given as $40$ cases, the average inventory level can be calculated as half of the order quantity:

Therefore, the answer is approximately $45.$ So$,$ the correct answer is:

B$.45$

Explanation:

Store A$\text{'}$s average inventory level is calculated using the Economic Order Quantity formula. With an order quantity of $40$ cases, the average inventory is approximately $45.$