A consumer has a utility function U = 10 x 0.2 y 0.8 , where x is the number of cups of coffee consumed, and y, the number of mini-cartons of ice…

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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

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