Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y) = x2 + 2y2 - 3xy; x+y=24 . . . There is a value of located at (x, y) = (Simplify your answers.)Page-1 (@21 ) cliveon, fly.y ) : 20- *2 92. let gc x. y ) = * +4y - 17 = 0 To find :: Extremum value Solution : by Lagrange's multiplier F (xiyit ) : f (x.y ) - a g (x.y ) & F ( Xy,a ) = 20-x2 y 2 - 2 ( x + 4y - 17 ) .. Platitially differentiate wirt n, yo I and equate to zero. 3 1 = 3 [ 2 0 - x 2 y 2 - a ( x tug - 1 ) ] = 0 2 [ 20 - x 2 g 2 - 2 ( x + 4g - 17) ] = 27 - 4 4 = 0 3 8=- 21 $ 1 2 0 x 2 - 8 2 - 2 ( x + ug - 1 7 ) ] . o ) . X4 44- 17 : 0 - 13 3) ( - 2 ) + 4 ( - 24 ) - 17 = 0 - d - 162 - 34 -0 - 17 : 39 2 1 = -2 Menu, n = - (- 2 ) . ) and y = - 2 ( - 2 ) = 4 Point of entremum is ( 1, 4 )Page. 2 Checking for maximumor minimum. and " ( - 2 : ) . 1 - 2 ) - 0 = 470 Do Hance (z n=1 ; y=y is Point of minimum. Therefore , minimum value is - f ( 1, 4) : 20- ( +12 - ( 4) : 20- 17 . 3 minimum Value = 1 3