Jade consumes two goods, X and Y. Her preferences are described by the utility function U(X,Y) = XY. The price of good X is $30 and the price of good Y is $45. Jade has $1200 dedicated to the purchase of these goods. 1. What is her optimal consumption of goods X and Y? 2. What is the total utility associated with this consumption bundle? 3. Suppose the price of good X increases to $45. What is Jade's new optimal consumption bundle? 4. Use this information to sketch Jade's demand for good X