A rectangular tank is to have its capacity of 1.0 cubic meter. If the tank is closed and the top is made up of a metal half as thick as its sides and base,use Lagrange method of undermined multipliers to determine the dimensions of the tank so that the total amount of metal used in its construction has minimum metal volume. Use LAGRANGE method to find dimensions of the tank.
2026-04-03 22:57:29.1775257049
using lagrange method of undetermined multipliers
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Hint
Start defining the inside dimensions of the tank (in meters) : length is $l$, width is $w$, height is $h$; let be $t$ be the thickness of the metal.
What are the areas for each of the faces ? From that, what is the corresponding amount (volume of metal) of each face ? What is the total volume of metal ? This is what you want to minimize subject to the constraint that $l\times h\times w=1$.
I am sure that you can take from here.