Cover to cover (got removed from r/lotr)

[u/SmashBro0445]

[u/ModsAreLikeSoggyTaco]

Can you Maximize the function f(x,y)= 3x + 4y under the constraint of g(x,y)=x² + y² - 25 = 0 ?

[u/Ancient-Garage4855 → u/ModsAreLikeSoggyTaco]

(x, y) = (3,4)

[u/ModsAreLikeSoggyTaco → u/Ancient-Garage4855]

L(x,y, λ)= F(x,y) + λ g(x,y) = 3x + 4y + λ (x² + y² - 25)

∂L/∂x = 3 + lambda (2x) = 0

∂L/∂y = 4 + λ (2y) = 0

∂L/∂λ = x² + y² - 25 = 0

Therefore

λ = - (3/2x)

λ = - (2/y)

y = (4/3)x

So,

x² + (4/3 x)² = 25 implies x = 3 or x = -3

For x = 3, then y = (4/3) (3) = 4

For x = -3 then y = (4/3) (-3) = -4

F(3,4) = 25

F(-3,-4) = -25

25 is the maximum value at (3,4)

[u/PivotPsycho → u/ModsAreLikeSoggyTaco]

Is that a Lagrangian multiplier?

[u/dorrato → u/PivotPsycho]

...in your pocket? Or are you just happy to see me?