Neco 2019 Commerce Question 10

Three product categories A, B and C are stored in a warehouse. Their annual demands are \(D_A=40\,000\) units, \(D_B=50\,000\) units and \(D_C=60\,000\) units. Unit costs are ₦80, ₦50 and ₦30 respectively. The holding‑cost rates are 25 % for A, 20 % for B and 15 % for C. The ordering cost per order is the same for all items, ₦4\,000. Because of space limitations the total average inventory cannot exceed 10\,000 units, i.e. \(\frac{Q_A+Q_B+Q_C}{2}\le 10\,000\). Assuming independent EOQ calculations but adjusting the order quantities to satisfy the space constraint, determine the optimal order quantities \(Q_A, Q_B, Q_C\) that minimise total annual cost, and compute that minimum total annual cost (including purchase, ordering and holding costs). Give the order quantities rounded to the nearest whole unit and the total cost rounded to the nearest naira.