please show work and explain! thank you.

Problem 3 There are two goods 1 and 2. Denote by (X1, T2) the consumption bundle consisting of x1 units of good 1 and x2 units of good 2. Arya loves to consume both goods, however, only in a fixed proportion. She always consumes 4 units of x2 for every unit of x1. 1. Write down the utility function that represents Arya's preferences. Draw the indifference curve going through the point (2,2). In the same diagram, draw the indifference curve along which Arya's utility is 4. Determine Arya's marginal rate of substitution (MRS). Does Arya have Diminishing Marginal Rate of Substitution? 2. Are Arya's preferences monotonic? Are they strictly monotonic? Does Arya exhibit convex preferences? Are Arya's preferences strictly convex? 3. Suppose that the price of good 1 is 2 and the price of good 2 is 1. Arya has 6 dollars to spend for her consumption. Write down the equation for her budget line. Draw the budget line in a diagram. Determine the most preferred consumption bundle (x], x7) that Arya can afford. Illustrate her optimal choice in the same diagram