Need a detailed procedure. Thx

QUESTION 3 Consider a consumer who wises to maximize her utility function, U(x,y) = 100-ex -e-y, by choice of goods x and y, and who faces a budget constraint B(Px,Py,m) = {(x,y) = Ripxx + py = m}, where m, px and py respectively denote nominal income, the price of good x and the price of good y. It is assumed that (m,x,y) ERA. (a) i) State sufficient conditions for the existence of a global maximum for this problem. ii) Are these sufficient conditions satisfied? Briefly explain. (b) i) Write down the Lagrangean function for this problem. ii) Derive the values of x and y at which the Lagrangean is stationary. (c) Derive the bordered Hessian matrix for this problem. (d) Prove that any stationary point of the Lagrangean is an interior global maximum for this problem. (e) Prove that the consumer's demand functions that you derived in (c) are homogeneous of degree zero in prices and income