An adult female lion requires about 6kg of meat per day and has a gut capacity of about 30kg;which means that, with a full gut at the end of the day,...

An adult female lion requires about 6kg of meat per day and has a gut capacity of about 30kg;which means that, with a full gut at the end of the day, it can go five additional days without eating. Zebras have an average edible biomass of 164kg, large enough to meet the food demands of many lions. If a female lion selects to hunt in a group, the probability of successful kill per chase has been observed to increase with group size to a point, and that each chase consumes 0.5kg of energy. Suppose that the probabilities of a successful hunt are given by p(1)=0.15, p(2)=0.33, p(3)=0.37, p(4)=0.4, p(5)=0.42, p(>=6)=0.43, when p(n) represent the kill probability per chase for lions hunting in a group of size n. Formulate this as an MDP, in which the state represents the lion's energy reserves at the end of the day, the action is to hunt and in what size group. Assume one hunt per day and the lion's objective is to maximize its probability of survival over T days. Also, if a hunt is successful, lions in the huntiong group share the meat equally and the initial state=5kg(reserve at the begging of the first day).