tentukan nilai x dan y untuk fungsi minimum c ( x,y ) = x² + 3x - 6y, dimana x + y = 42

jawab


x + y = 42
y = 42 - x

c(x,y) = x² + 3x - 6y
c(x,y) = x² + 3x - 6(42-x)
c(x) = x² + 3x - 252 + 6x
c(x) = x² + 9x - 252
c'(x) =  0
2x + 9 = 0
x = - 9/2
y = 42 - x
y = 42 + 9/2 = 93/2

c(x,y) = x² + 3x -6y
= (-9/2)² + 3(-92/2) - 6(93/2)
= 81/4 - 276/2 - 279
= -396 ³/₄