Neco 2024 Commerce Question 23

A warehouse charges a base monthly rent of \(\text{₦}150,000\) for up to 500 cubic metres. Each additional cubic metre costs \(\text{₦}350\). A handling fee of 2 % of the value of goods stored per month is also applied. A retailer wishes to store 800 cubic metres of goods worth \(\text{₦}12,000,000\). The retailer can split the stock between this warehouse (Warehouse A) and a second warehouse (Warehouse B) that charges a flat rate of \(\text{₦}200,000\) for up to 600 cubic metres and \(\text{₦}300\) for each extra cubic metre, with a handling fee of 1.5 % of the value of goods stored there. Assuming the value of goods is proportional to the volume stored in each warehouse, what allocation of volume between the two warehouses minimises the total monthly cost, and what is that minimum cost? Express the cost in Naira to the nearest thousand.