Gce Model Questions Vol1 2020 Geography Question 30

A region is exposed to volcanic ash fall and flooding over a 10‑year planning horizon.\n\n• Volcanic eruptions follow a Poisson process with mean \(\lambda = 0.12\) per year. If an eruption occurs, the average ash damage is £8 million. Installing a volcanic‑mitigation system costing £m million (where \(0\le m\le5\)) reduces the damage by a factor \(e^{-m}\).\n\n• Floods occur each year with probability 0.03 and cause average damage of £5 million. Flood‑mitigation costing £f million (where \(0\le f\le5\)) reduces the flood probability linearly by 0.004 per £1 million invested, but the probability cannot fall below 0.01.\n\nThe total mitigation budget is £6 million (so \(m+f=6\)). Using a discount rate of 5 % per year (present‑value factor for year \(t\) is \((1.05)^{-t}\)), determine the allocation \((m, f)\) that minimises the present value of the expected total cost (mitigation investment plus discounted expected losses). State the optimal allocation (to one decimal place) and the minimum present value (in £ million, to two decimal places).