Please help me solve this constrained optimization in two variables problem. I can't paste the format so I attached the question as a picture.

4 Constrained optimization in two variables Anthony seeks to maximize the following utility function We 1/) = w1/3y2/3 subject to the budget constraint palm + my = I Where pm, py, m, y, I > 0. a) Find Anthony's utilitymaximizing bundle (1B*, y*) as a function of pm, py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on 31:? What share is spent on y? In other words, calculate pfo and 21113;. Are these shares a function of prices? Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in px on Anthony's utility? e) When is a reduction in pa; better for Anthony than a reduction in pg of the same size? Hint: use the envelope theorem