Calculating utility, with graph

You are choosing between two goods, X and Y, and your total utility from each is shown below.

Units    TUx     TUy
  1       10      8
  2       18      15
  3       24      21
  4       28      26
  5       31      30
  6       33      33

a.  If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase in maximizing utility.

b.  Specify the amount of total utility you will realize.

c.  Assume that, other things remaining unchanged, the price of X falls to $1.  What quantities of X and Y will you now purchase?

d.  Using the two prices and quantities for X, graphically derive a demand curve for X.