Imagine there are two goods, X and Y. The utility function is: U = XY. The price of X is $2 and the price of Y is $4. The budget is $20. What is the optimal quantity of X and Y to consume?

Imagine there are two goods: books and coffees. Your utility function is U = BC, where B is the number of books you consume and C is the number of coffees you consume. If your budget is $40, the price of books is $10, and the price of coffees is $4, how much of each good will you consume?

Please show work and explain the method behind finding utility and all steps involved.