Perfect Complements: Suppose that a consumer has perfect complements (or Leontief) preferences over bundles of non-negative amounts of each of two commodities. The consumer's preferences can be represented by a utility function of the form U(x1, x2) = min(x1, x2). 1. Illustrate a representative indifference curve for the consumer. (Hint consider the cases where x1 > x2 and x2 > x1 seperatley. 2. Indicate the direction of increasing utility for the consumer. 3. Are these preferences strictly convex? Explain why. 4. Are these preferences convex? Explain why.