1. A consumer has a utility function U = 10 x0.2y0.8, where x is the number of cups of coffee consumed, and y, the number of mini-cartons of ice cream.
a) Derive expressions for ∂U/∂x and ∂U/∂y.
b) Prove that U = x. ∂U/∂x + y. ∂U/∂y, and show that this expression is homogeneous of degree 1
I need a clear answer with all steps please thx