Neco Model Questions Vol1 2019 Civic Education Question 40

A peace‑building initiative has a fixed budget of ₦20 million to be split between two components: community dialogue (C) and economic development (E). Let \(x\) million naira be allocated to C, so \(20-x\) million goes to E. The probability that C succeeds is \(p_C = 0.4 + 0.03x\) (capped at 0.9) and the probability that E succeeds is \(p_E = 0.5 + 0.02(20-x)\) (capped at 0.9). The two components succeed independently, and peace is achieved only if both succeed. The monetary benefit of achieving peace is estimated at ₦100 million. Determine the integer value of \(x\) (in millions) that maximises the expected net benefit (expected benefit minus the fixed cost). State the optimal allocation as "\(x\) million to C and \(20-x\) million to E".