It seems reasonable to require "real world" conditions. Non-zero prices, whole cent prices, integral chickens per sale, non-negative chickens per sale, etc. Wit

It seems reasonable to require "real world" conditions. Non-zero prices, whole cent prices, integral chickens per sale, non-negative chickens per sale, etc. With those, the solution is unique, and in part, that's what makes this problem interesting, hard, surprising, and with its own elegance.