Neco 2022 Agricultural Science Question 27

In a teak plantation, the volume \(V\) (m\(^3\)) of a tree is estimated by \(V = 0.00045 D^{2} H\), where \(D\) is the diameter at breast height in centimetres and \(H\) is the total height in metres. Height is related to diameter by \(H = 0.75 D + 5\). The stand consists of twelve trees with diameters (cm): 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68 and 72. Timber sells for \(\text{₦}1500\) per m\(^3\) and the cost of harvesting a tree is \(\text{₦}200\) plus \(\text{₦}5\) per centimetre of its diameter. To protect the forest, the total volume harvested must not exceed 40 % of the stand's total volume. Which trees should be harvested to maximise net profit and what is that maximum profit (rounded to the nearest naira)?