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.