Neco 2020 Government Question 10

A local government receives its annual federal allocation according to the formula \(\text{Allocation}=K\bigl(\alpha P+\beta A+\gamma F\bigr)\), where \(P\) is the population, \(A\) is the land area (km\(^2\)), \(F\) is the fiscal performance index (a number between 0 and 1), and the weights satisfy \(\alpha+\beta+\gamma=1\) with \(\alpha=2\beta\). The constant is \(K=120\). In the current year the data are: \(P=250\,000\), \(A=500\), \(F=0.80\) and the allocation received is \(\text{₦12,000,000}\). (a) Determine the value of the weight \(\beta\). (b) If the population rises by 10 % (to 275 000), the area remains the same, and the fiscal index improves to 0.90, what will be the new allocation (in naira) assuming the same \(K\) and weights?