Neco 2017 Government Question 4

A local government council receives three revenue sources: Property Tax (P), Market Levy (M) and a Federal Allocation (F). The relationships are \(P = 0.4F\) and \(M = 0.3F\). Total revenue \(R = P + M + F\) is allocated as follows: Salaries \(S = 0.5R\), Infrastructure \(I = 0.3R\), Community Services \(C = 0.2R\). The council decides to set aside an additional development fund equal to \(10\%\) of total revenue, taken entirely from the Community Services budget, reducing \(C\) accordingly. After this reallocation, Community Services must still be at least \(\text{₦}20\) million. What is the minimum Federal Allocation \(F\) (in millions of naira) that satisfies all conditions? Give your answer to two decimal places.