Question

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.

Answer 1

Answer:

The Dimension of the rectangular box of maximum volume  is

(x,y,z) = $(\frac{a}\sqrt{3}$   $, \frac{b}\sqrt{3}$  $, \frac{c }\sqrt{3}$  $)$ .

Step-by-step explanation:

It is in the following attachment