∇x,y,λ=(∂x∂V,∂y∂V,∂x∂V)=0
Take partial derivatives of V(x,y,λ)=xy+λ(2,000−20x−10y)
∂x∂V(x,t,λ)=y−20λ
∂y∂V(x,t,λ)=x−10λ
∂λ∂V(x,t,λ)=2,000−20x−10y
Finally, we get the system of equations
⎩⎨⎧y−20λ=0x−10λ=02,000−20x−10y=0
Solve this system:
⎩⎨⎧y=20λx=10λ2,000−200λ−200λ=0
⎩⎨⎧y=20λx=10λ400λ=2,000
⎩⎨⎧λ=5x=50y=100
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