2. We consider the allocation of m indivisible items to n agents, in order to maximize the sum of valuations (a) Suppose each agent i is interested in precisely one subset Si of the m items; her value for Si or any superset of S isv20, and her value for any other set of items is 0. Given all the Si's and vy's as input, show that an allocation T T that maximizes the total values is NP-hard to compute. (By total value we mean the sum of the agents' values for their allocated subsets.) (b) Suppose each agent i has value vij) for each item j, and then for any subset Si her value is min( jess(j), Bi}, where Bi can be seen as some budget. Given all vi(j)'s and Bi's as input, show that an allocation Ti,-.. ,Tn that maximizes the total values is NP-hard to compute. 2. We consider the allocation of m indivisible items to n agents, in order to maximize the sum of valuations (a) Suppose each agent i is interested in precisely one subset Si of the m items; her value for Si or any superset of S isv20, and her value for any other set of items is 0. Given all the Si's and vy's as input, show that an allocation T T that maximizes the total values is NP-hard to compute. (By total value we mean the sum of the agents' values for their allocated subsets.) (b) Suppose each agent i has value vij) for each item j, and then for any subset Si her value is min( jess(j), Bi}, where Bi can be seen as some budget. Given all vi(j)'s and Bi's as input, show that an allocation Ti,-.. ,Tn that maximizes the total values is NP-hard to compute