Please show thorough work thank you!

2. Owen has preferences represented by the following utility function: U(x, y) = 2ln(x) ty (a) 10 points Suppose Owen faces prices Pr = 6 and Py = 3 with income, m = 9. Find Owen's optimal bundle: (b) 5 points Suppose Owen's income falls to m = 6 while prices fall to pr = 2 and Py = 1. Find Owen's optimal bundle: (c) 5 points Suppose Owen's income falls to m = 4 and the prices become pr = 2 and py = 3. Assuming no further price changes, at what level of income, if any, will Owen buy Good Y