Question 3 (12 marks) Consider the function f (x. y) = xy subject to the constraint x +9 =16. a. Write down the constraint equation (x, y ) =0 and the Lagrangian L(x, y, a ) = f (x, y) - Ad(x, y). (2 marks) b. Find L and Ly - (2 marks) C. Solve the equations L = 0 1 =0 $(x, y) =0 for x , y and 2 . There are four distinct solutions. When you have found the values, write them up in a table in the form given below, where each row corresponds to a distinct solution of the equations. X f (x, y ) Min/Max (6 marks) d. Find the value of f (x. y) at each point from part (c). Add these values to your table from part (c) and label them as being maximum or minimum values of the function subject to the constraint. Note: you do not need to use a 2nd derivative test