Jack likes cookies (c) and milk (ml). He always takes one cup of cookies with two cups of milk. Both cookies and milk cost $2 per cup. Jack has $24 to spend on these two goods. Consider a price drop in milk to $1 per cup. (Provide detailed explanations for the following parts)

a. What kind of preferences does Jack have? Illustrate the shape of his indifference curves (cookies are measured on the y-axis).

b. Derive his demand functions for cookies and milk.

c. Find his optimal consumption bundle before and after the price change and write his budget constraint before and after the price change.

d. Calculate the substitution effect and the income effect of the price change in Jack's demand of milk.