Please solve the question clearly providing a step by step explanation on how to do it. Do everything the question asks you to do. Do not miss anything out.

This problem set tells the story of three friends Alice, Bob, who are consumers, and C arol, who owns a firm. Alice, and Bob have preferences over two goods, Dumplings and Free time. Each of them have Ti available hours each day with i=A,B. Carol's firm produces dumplings using two inputs, L abour and K apital with respective prices w and r. Denote the market price of dumplings as p. 3. [12 points] Like Alice, Bob has no other source of income apart from the work he does for Carol's firm. But Bob is a very particular person. He likes to eat exactly three dumplings every hour of free time he enjoys, not more, not less. Without drawing any graph, argue whether his preferences are monotone. Write a utility function that represents Bob's preferences over dumplings and free time. Find Bob's demand of dumplings and labour supply as a function of TB,p and w under that utility function