Find the optimum commodity purchases for a consumer whose utility function and budget constraints are U=(x^1.5)(y) and 3x+4y=100 respectively.
a. Show that the first-order conditions for a constrained utility maximum with this function require individuals to choose goods in the proportion: X/Y=(Px/Py)^1/(d-1)
b. Show that the result in part (a) implies that individuals will allocate their funds equally between X and Y for the Cobb-Douglas case (d=0)