Is it permissible to announce to customers that a portion of the product's price will go to the poor and needy, with the intention of encouraging them to buy, and with the genuine intention of donating?

The reward of a merchant is determined by their primary intention. If the primary intention is to donate to the poor, and promoting the merchandise is secondary to that, then they will have a reward according to their intention, for the Prophet (peace be upon him) said: "Deeds are only by intentions, and every person will have what they intended." However, if their primary purpose is to sell and promote their merchandise, then they will only have what they intended.