Given the production function y = f(x1, x2) = min {x1, x2}: (a) Find the profit-maximizing factor demand functions. (5 points). (b) Find the supply function.(5 points) (c) Find the profit function. (5 points) (d) Demonstrate the degree of homogeneity of the profit function. (5 points) (e) Is the Hessian matrix of the profit function positive or negative semi-definite? Demonstrate. (5 points) (f) Demonstrate Hotelling's lemma. (5 points)