What is the total annual inventory cost when EOQ is used in the mountain bikes scenario?

• A. $110,000
• B. $112,800
• C. $115,000
• D. $117,000

Answer: (B)

When you use the EOQ approach, the total annual inventory cost you care about is the sum of the holding cost and the ordering cost. The movement is to pick an order quantity that balances these two so the sum is smallest.

The EOQ itself is Q* = sqrt(2 D S / h), where D is annual demand, S is cost per order, and h is the holding cost per unit per year. The annual holding cost at this quantity is h Q*/2, and the annual ordering cost is D S / Q*. If you substitute Q* into those two expressions, you get equal values for holding and ordering costs: each equals sqrt(D S h / 2). Adding them gives the total annual cost for these two components: 2 * sqrt(D S h / 2) = sqrt(2 D S h).

If the unit purchase price is constant, the purchase cost PD is fixed and can be added to get the full total annual inventory cost: total = PD + sqrt(2 D S h).

In the mountain bikes scenario, plugging the given data into these formulas yields a total of $112,800. This reflects the combined minimum annual holding and ordering costs (plus any fixed purchase cost if applicable).