Abby likes tangerines and oranges. For every 4 tangerines, Abby is equally happy to consume 2 oranges instead. Let x be the number of tangerines, and y be the number of oranges.

(a) (5 pts) Graph Abby's indifference curves. Make sure to mark the direction of the preferred bundles.

(b) (5pts) Write down an utility function that represents Abby's preferences.

(c) (5pts) Write down another utility function different from your previous answer but also represents Abby's preferences.

(d) (5pts) Does v(x, y) = x + y represent Abby's preferences?

(e) (5pts) What is Abby's marginal rate of substitution?

(f) (5 pts) Suppose that px = 1, py = 1, and Abby has Y = 20. Compute Abby's optimal consumption bundle.