A company faces an annual demand of 12,000 units. The ordering cost is $\text{₦}4,500$ per order. Holding cost is 25% of the unit cost per year. The supplier offers quantity discounts as follows:\n- 1-1,000 units: unit cost $\text{₦}1,200$\n- 1,001-3,000 units: unit cost $\text{₦}1,150$\n- 3,001-6,000 units: unit cost $\text{₦}1,100$\n- 6,000 units: unit cost $\text{₦}1,050$\nDetermine the order quantity that minimises the total annual cost (ordering + holding + purchase) and compute that minimum total cost.

Question

A company faces an annual demand of 12,000 units. The ordering cost is $\text{₦}4,500$ per order. Holding cost is 25% of the unit cost per year. The supplier offers quantity discounts as follows:\n- 1-1,000 units: unit cost $\text{₦}1,200$\n- 1,001-3,000 units: unit cost $\text{₦}1,150$\n- 3,001-6,000 units: unit cost $\text{₦}1,100$\n- >6,000 units: unit cost $\text{₦}1,050$\nDetermine the order quantity that minimises the total annual cost (ordering + holding + purchase) and compute that minimum total cost.

Accepted Answer

Order quantity = 6,001 units; Minimum total cost ≈ ₦13,396,630

Neco Model Questions Vol1 2022 Commerce Question 15

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