Question

Find the minimum value of x²yz³ subject to condition 2x + y + 3z =1​

Answer 1

x²+ý²×z³=785545&;:%^&&

Answer 2

To find the minimum value of x²yz³ subject to the constraint 2x + y + 3z =1, we can use the method of Lagrange Multipliers.

The method of Lagrange Multipliers is used to optimize a function subject to a constraint.

The Lagrangian function is defined as: L(x,y,z,λ) = $x²yz³ + λ(2x + y + 3z - 1)$

where λ is a Lagrange multiplier.

The goal is to find the critical points of the function, which are the points where the partial derivative of L with respect to x, y, z, and λ are equal to zero.

∂L/∂x = 2xyz³ + λ(2) = 0

∂L/∂y = x²z³ + λ(1) = 0

∂L/∂z = x²yz² + λ(3) = 0

∂L/∂λ = 2x + y + 3z - 1 = 0

Solving this system of equations gives us:

x = 0, y = 0, z = 0 and λ = 0.

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