Suppose that the consumer has the following utility function: u(x1, 12) = 11 12 The prices of good I and good 2 are given as p1 and p2, and the income of the consumer is m. (a) What is the budget constraint of the consumer? (b) Based on her utility function and budget constraint, derive her demand functions for good I and good 2. (c) Draw the income offer curve. (d) Draw the Engel curve for both goods. (e) Suppose m = $100. Draw the demand curve for both goods with price on the vertical axis and quantity on the horizontal axis