The campus bookstore sells 4,000 sets of graduation regalia each year. placing an order from their supplier costs $25 regardless of order quantity, so they usually place a large order (a half year's supply) at a time. it costs $5 per year to hold a cap and gown in inventory, primarily insurance costs for the highly flammable material. what is their optimal order quantity?

The optimal order quantity will be 200

Explanation:

The formula is the following:

The Math involving how to reach this formula finds their base on differential analysis maths, so it is beyond the scope of the question.

Now, let's focus on what using this method does to the university if implement:

It is quite easy to calculate so if the cost change or the annual demand changes, then it will be easy to find the new optimal quantity

It is important to consider that the demand must be steady during the year. This method does not fit when there is seasonal demand for the product or if there are punctual buyers of high volume. The method also has a problem with the time to replenish the inventory, because it is assuming it happens instantly. Also, it is important to notice that the units purchase cost is not in the calculation, so if a higher purchase volume gets discounts, it is not in being considered in this formula.

So resuming,

The formula you should remember in case to calculate the cost will be this:

Total cost= cost to order + Cost of inventory

In this case will be cost to order = 20 request (4000 demand / 200 order) *$25 each = 500

cost of inventory = 200 * 5 = $1000

Total of $1,500