SHOW COMPLETE SOLUTION.

A barangay captain is running for reelection. He has a fund of PhP100,000 which he can use for his campaign. He wants to launch his campaign to 5 zones of the barangay but due to limited fund he will only select which zone to launch his campaign to maximize the number of votes based on the population of the zone. The table below shows the voting population per zone and the corresponding fund needed to launch the campaign. The choice of the zone is to receive either all allotted funds or none.

ZONE	POPULATION (in hundreds)	REQUIRED FUNDS (in ten thousand Pesos)
1	46	4
2	30	2
3	45	5
4	29	3
5	25	2

START WITH ZONE 5 AS STAGE 5.

a) Define the Stage. _________

b) What is the State? _________

c) What is the Alternative or Action? _________

d) What is the value of the decision variable if the zone is selected? _________

e) What is the range of values of the state? _________

f) Starting with Zone 5 as Stage 5, what is the recursive equation? Max Z = ________

g) What is the recursive equation in Stage 3 (Zone)? Max Z = _________

h) What is the optimal maximum number of votes (in hundreds) the barangay captain is expected to get? _________

i) How many zones will not receive funds? _______ Which zones are these? Put NA for excess cells, if any. Answer in sequential order. Zone _____, Zone __________, Zone _________

j) How much fund (in ten thousands) remains not used in the campaign? _________