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Use Lagrange multipliers to find the dimensions of a rectangular box of maximum volume that can be inscribed (with edges parallel to the coordinate axes) in the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1.

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muhammadalambsmathf1

Answer:

The Dimension of the rectangular box of maximum volume  is

(x,y,z) = [tex](\frac{a}\sqrt{3}[/tex]   [tex], \frac{b}\sqrt{3}[/tex]  [tex], \frac{c }\sqrt{3}[/tex]  [tex])[/tex] .

Step-by-step explanation:

It is in the following attachment                          

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