1. (45 points) A consumer consumes three commodities x, y, and z in nonnegative quantities. Her utility function is given by 1 u ( x, y, z ) = zz + - log(x) + - log (y). She has wealth of 2 and faces prices Px = Py = 7, Pz = V2. Her utility maximization problem is thus given by max u (x, y, z) s.t. =x + y + z v2 0, z 20. 2 How much of each good will she purchase? Hint: log (2) ~ 0.7; log(1) = 0