80 points) A consumer has the utility function : u(x,y) = 5.x2 + 6xy + y2 +380 +18y (a) (20 points) Determine the marginal utiliy for the two commodities. (b) (20 points) The consumer has a budget of 40 dollars. A unit of x costs 10 dollars and a unit of y costs 5 dollars. Write down the budget equation. (c) (20 points) The consumer wants to maximize his utility subject to his budget con- straint. Write down the Langrangian for this problem. (d) (20 points) Solve the Langrangian problem and write down which points are the optimum