For each of the utility functions below, sketch the indifference curve for utility level 24 and indicate the direction of the weakly preferred set.

(1, 2) = 31 + 2

(1, 2) = min{min{1, 22}, min{21, 2 }}

For the utility function (1, 2) = ln(1 ) + 2, derive the marginal rate of substitution. [Assume that x1 is measured on the horizontal axis.]