A wholesaler orders a product with an annual demand of 12,000 units. The ordering cost is ₦2,500 per order. The holding cost is 20\% of the unit cost per year. The supplier offers the following price schedule:

- 1-199 units: ₦1,200 per unit
- 200-499 units: ₦1,150 per unit
- 500 units or more: ₦1,080 per unit

Assuming the wholesaler orders the same quantity each time, determine the order quantity that minimizes the total annual cost (ordering + holding + purchase cost). Provide the optimal order quantity and the corresponding total annual cost.

Question

A wholesaler orders a product with an annual demand of 12,000 units. The ordering cost is ₦2,500 per order. The holding cost is 20\% of the unit cost per year. The supplier offers the following price schedule:

- 1-199 units: ₦1,200 per unit
- 200-499 units: ₦1,150 per unit
- 500 units or more: ₦1,080 per unit

Assuming the wholesaler orders the same quantity each time, determine the order quantity that minimizes the total annual cost (ordering + holding + purchase cost). Provide the optimal order quantity and the corresponding total annual cost.

Accepted Answer

Optimal order quantity: 527 units; Minimum total annual cost: ₦13,073,841

Neco 2018 Commerce Question 40

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