11. The selling price of a commodity is an integer number of yuan. 100 yuan can buy at most 3 pieces. Person A and Person B each brought several hundred-yuan bills. The money A brought can buy at most 7 pieces of this commodity, and the money B brought can buy at most 14 pieces. When the two people's money is combined, they can buy 1 more piece. The price of each piece of this commodity is yuan.
【Analysis】100 yuan can buy at most 3 items, so the price of the goods is between 26 yuan and 33 yuan (including 26 yuan and 33 yuan), because if it is less than 25 yuan, then 4 items can be bought, and if it is more than 33 yuan, then 3 items cannot be bought. Person A can buy at most 7 items with the money they have, so A has 200 yuan (100 yuan can only buy 3 items, and 300 yuan can buy at least 9 items), and the price of the goods is between 26 yuan and 28 yuan (including 26 yuan and 28 yuan), because if it is more than 29 yuan, then 7 items cannot be bought. Person B can buy at most 14 items with the money they have, so B has 400 yuan (200 yuan can buy at most 7 items, and adding another 100 yuan can buy at most 3 + 1 = 4 more items, making only 11 items, while 500 yuan can buy at least 15 items), and the price of the goods is between 27 yuan and 28 yuan (including 27 yuan and 28 yuan), because if it is less than 26 yuan, then 15 items can be bought.
Finally, when A and B's money is combined, a total of 600 yuan can buy 22 items. It is found that if the price is 28 yuan, the total amount exceeds 600 yuan, so only 27 yuan meets all the requirements.
In summary, the price of each item of this product is 27 yuan.