Homework Soursefxy20x32y subject to the constraint of xy60Solution xy 60 x
f(x,y)=20x^3/2y subject to the constraint of x+y=60
Solution
x+y = 60 x = 60-y f(x,y)=20x^3/2y f(x,y) = 20y(60-y)^3/2 f_y = 20(60-y)^3/2 - 30y(60-y)^1/2 f_y = 10(60-y)^1/2 [2(60-y) - 3y]=0 10(60-y)^1/2 [120-5y] = 0 y = 24 hence x = 36 f(36,24) = 20(36)^3/2 * 24 f(36,24) = 20*216*24 f(36,24) = 103680.......maximum value
