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Unformatted text preview: order condition fails but there is clearly a maximized value y * = 6 . Ignore this example and stick to our F.O.C and S.O.C) (6) y = lnx + lny subject to 5 x + 3 y = 30 . Solution: (1) L = lnx + lny + λ (305 x3 y ) F.O.C.: ∂ L ∂x = 1 x5 λ = 0 ; ∂ L ∂x = 1 y3 λ = 0 ; ∂ L ∂λ = 305 x3 y = 0 . Solve the two ﬁrst order conditions: x = 1 5 λ and y = 1 3 λ . Plug into the third one: 302 λ = 0 . λ = 1 15 . So x = 3 and y = 5 . (2) y = lnx + ln ( 305 x 3 ) F.O.C. dy dx = 1 x + 3 305 x (5 3 ) = 0 . So x = 3 and y = 5 . 2...
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 Summer '10
 Raven
 Derivative, dx, dy, Bin Xie

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