The ASG Rebels wish to truck supplies to a border outpost which is expecting an attack by the Philippine Army within hours. The nearest supply depot is connected to the outpost by two separate roads, one running through forests and the other over flatlands. A supply convoy moves faster over flatlands route but enjoys better camouflage on the forest route. The convoy must take one route or the other. The Philippine Army anticipates a supply effort along one of the routes, and plans to hinder it with air strikes. It has available a single squadron of airplanes, which cannot be divided. If the Army sends its airplanes above the forest route and finds ASG Rebels there, the Army will have time for five strikes against the convoy. If the army sends its airplanes above the flatlands route and the rebels are using that route, the army will have time for four strikes. If the army sends its planes over the wrong route, valuable time is lost. Once it realizes its error and locates the convoy on the other route, the army will have time for three strikes on the flatlands route, but time for only one strike on the forest route. a) Develop the payoff table of this game problem. b) What is the type of game played by the two players and what is the estimated value of the game? c) Determine the optimal strategies of the Philippine Army and the ASG Rebels.