You made an assumption that I originally did, which is that farmer $FOO was dissatisfied with his sales because he had half of his stock unsold at the midday ma

You made an assumption that I originally did, which is that farmer $FOO was dissatisfied with his sales because he had half of his stock unsold at the midday mark. This assumption is unsupported by the text of the problem. Try relaxing it. Also, chickens are integers but prices are not is a core insight. Life gets easier if you solve a related problem which forces prices to be integers as well, such as an alternate universe where chickens are priced in nickels.