Question-1 Consider the following problems (18 marks) (a) max , x , y x' + y subject to r2

Question-I Consider the following problems maxxyx + y subject tor < 2x +6y Ss with 0 < r < s (b) minx y x + y subject to r 2 2x2 +6y2 s2 with 0 < r < s (18 marks) (ii) (iii) (iv) (v) Solve problem (a) Solve problem (b) How much does the optimal value of the function change if s changes by .1 unit in problem (a). How much does the optimal value of the function change if r changes by .1 unit in problem (a). Check the second order condition for problem (b). What are the geometric interpretations of (a) and (b)?