Gce Model Questions Vol1 2018 Commerce Question 4

A warehouse stores two products, A and B. The unit cost of A is ₦800 and its annual holding cost rate is 15 %; the unit cost of B is ₦500 and its annual holding cost rate is 10 %. The annual ordering cost for a joint order (containing both products) is ₦2 000, irrespective of the quantities ordered. Annual demand is 9 600 units for A and 4 800 units for B. The warehouse has a total storage capacity of 12 000 units (combined A and B). Assuming that the two products are ordered together in each joint order and that the proportion of each product in the order must reflect its proportion of total annual demand, determine the order quantities \(Q_A\) and \(Q_B\) (in units) that minimise the total annual inventory cost (holding + ordering) while satisfying the capacity constraint \(Q_A+Q_B\le12 000\). Give your answer as the nearest whole unit for each product.