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Math Help - constrained optimisation problem

  1. #1
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    Question constrained optimisation problem

    (a) Write down the objective function and the constraint equation for aconstrained optimisation problem which is to minimize the total surface area of a rectangular box with the constraint that its volume is fixed to be 1. (Hint: Let the box have length x, width y and height z.)

    (b) Solve the problem using the method of Lagrange multipliers.

    Is anyone teach me how to do this question? thanks
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  2. #2
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    Quote Originally Posted by lin.13579 View Post
    (a) Write down the objective function and the constraint equation for aconstrained optimisation problem which is to minimize the total surface area of a rectangular box with the constraint that its volume is fixed to be 1. (Hint: Let the box have length x, width y and height z.)

    (b) Solve the problem using the method of Lagrange multipliers.

    Is anyone teach me how to do this question? thanks
    To start you off, you are required to:

    \textrm{Minimise }\,2xy + 2xz + 2yz

    \textrm{subject to }\,xyz = 1.
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  3. #3
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    To minimize F(x,y,z), subject to G(x,y,z)= constant, use \nabla F= \lambda \nabla G where \lambda is the "Lagrange multiplier". Setting components equal gives three equations in the four unknowns, x, y, z, and \lambda. The constraint G(x,y,z)= constant is a fourth equation.

    Since the value of \lambda is not part of the solution, I find that dividing one equation by another to eliminate \lambda is often a good first step.
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