Suppose that there are two goods in the economy, and the price of each good is equal to 1. When Alice has income of $10, She consumes 1 unit of good y and 9 units of good r. As her income increases, she continues to buy just one unit of good y and spends the rest of her income on good x. Verify that the utility function U(x,y) = x+log y represents Alice\'s preferences? Show all your work. (Hint: Find the demand function for good x and y) under the assumption that the price of the good x is Px, the good y Py and the income is I.)