Improved Hardness Results for Profit Maximization Pricing Problems with Unlimited Supply

We consider profit maximization pricing problems, where we are given a set of m customers and a set of n items. Each customer c is associated with a subset S c ⊆ [n] of items of interest, together with a budget B c , and we assume that there is an unlimited supply of each item. Once the prices are fixed for all items, each customer c buys a subset of items in S c , according to its buying rule. The goal is to set the item prices so as to maximize the total profit.

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