b) A consumer's utility function for goods x and y is given by: u = xy 2x Suppose Px = $2, Py = $1 and income = $6 per day. (i) Using the Lagrange multiplier method find the utility maximizing quantities of x and y and the total utility obtained per day. (7 Marks) (ii) Compute the marginal utility of x and marginal utility of y and show whether the conditions for equilibrium have been satisfied