*A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum*

## Question

## Question

*A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum*

## LaGrange’s Method Problems

- Find the minimum value of x^2+y^2+z^2 subject to the condition xy+yz+zx=3a^2
- Discuss maximum or minimum for x^3+y^3-3xy
- Find the maxima and minima values of the function f (x, y) =3x+4y on the circle x^2+y^2=1 using method of Lagrange’s multipliers
- Find the maximum and minimum values of x^2+y^2 subject to the condition 2x^2+3xy+2y^2=1
- If x, y, z are the angles of a triangle, find the maximum value of sin x sin y sin z
- A rectangular box open at the top is to have a volume of 32 cubic feet. Find its dimensions if the total surface area is minimum
- Show that the rectangular box of maximum value and a given surface area is a cube
- Find the volume of the largest rectangular parallelepiped that can be inscribed in the ellipsoid x^2/a^2 +y^2/b^2 +z^2/c^2 =1
- Find the dimensions of the rectangular box open at the top of maximum capacity whose surface is 432 sq.cm