Chuck likes to read philosophy books. She is perfectly indifferent between new and used philosophy books. Her utility function is (,) = + , where and are the number of new and used philosophy books she consumes, respectively. For each of the following two scenarios, draw Eleanor's budget constraint and determine how many new and used books she would purchase. For this question, assume philosophy books are infinitely divisible.

a) Chuck has a budget of $200 for philosophy books. New books cost $40 each, while used books cost only $25 each.

b) There is a price increase. Now, new books cost $45 and used books cost $30. In response, Eleanor now allocates a budget of $230 to philosophy books.

c) Which of the scenarios provides the higher utility for Chuck?

please don't give handwritten answers