Margaret has utility =3ln()+ over goods x and y.

a. Solve Margaret's utility maximization problem to find ordinary demand functions and .

Then, use the following income and price values: =30, =2, =2 to find her optimal consumption bundle (,). Draw the budget constraint and mark the optimal bundle on it.

b. Suppose the price of good y increases: =5. If she received enough extra money to stay as happy as before, how much of each good would Margaret buy? How much extra money would she need? In the graph above, show the new point and the budget line it is on