(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 minimize F(x,y,z), subject to G(x,y,z)= constant, use where is the "Lagrange multiplier". Setting components equal gives three equations in the four unknowns, x, y, z, and . The constraint G(x,y,z)= constant is a fourth equation.
Since the value of is not part of the solution, I find that dividing one equation by another to eliminate is often a good first step.