Neco 2020 Government Question 6

Three development programmes A, B and C are evaluated by the Ministry of Public Administration using the overall effectiveness score \(E = w_{1}\,(\text{output/target})_{A}+w_{2}\,(\text{cost efficiency})_{B}+w_{3}\,(\text{public satisfaction})_{C}\). The weights satisfy \(w_{1}+w_{2}+w_{3}=1\) and \(w_{1}=2w_{2}\). The observed data are: \((\text{output/target})_{A}=0.75\), \((\text{cost efficiency})_{B}=0.80\), \((\text{public satisfaction})_{C}=0.90\). The reported overall score is \(E=0.82\). (a) Determine the value of \(w_{2}\). (b) If programme A improves its output/target ratio to \(0.85\) while the other two indicators remain unchanged, what is the new overall effectiveness score?