"These white shoes are beautiful and cheap."
There is no clear distinction between these terms and the interpretation may vary from person to person. In general, 美丽 and 漂亮 are interchangeable and close to pretty. It is less likely to use 漂亮 other than concerning the appearance only. So we may use 漂亮 on a dress, on someone's make-up, on someone's features, and on someone's appearance as a whole. We usually do not say a natural scenery is 漂亮, but 美 or 美丽, or just 好. 漂亮 is also less used on things considered beautiful based on a specific aesthetic standard, e.g. a wall paper pattern can be 漂亮 but a modern art painting would seldom be described as 漂亮.
美 or 美丽 are also very close. We usually use 1 character 美 rather than 美丽 for something more breathtaking and not approachable, or based on a specific aesthetic standard.