6. (15 points) Chloe consumes only books (x) and video games (y). Her preferences can be represented by the following utility function: U (x, y) = xyz. The price of books is 2, the price of video games is 2, and Chloe has an income of 30 dollars. Suppose Chloe has one "buy 10-get-10-free\" coupon for books (that is, she will get 10 free books if she buys at least 10 books). How many books and how many videogames will Chloe consume