The Lion 102
New member
- Joined
- Dec 31, 2020
- Messages
- 6
Show that a rectangular box with a top and fixed surface area has the largest volume if it is a cube.
The surface area of the box is given by 2(xy+xz+yz)=a
The volume of the box is given by V=xyz
I isolated z from the first equation, then I calculated the partial derivative of z with respect to x and y and set them to zero.
The problem is I got a complicated system of equations that was hard to solve.
This question was before the part about Lagrange multipliers, so is there another way to solve it.
I also noticed that the two equations were symmetric, so would that imply that x and y are interchangeable and might be equal?
The surface area of the box is given by 2(xy+xz+yz)=a
The volume of the box is given by V=xyz
I isolated z from the first equation, then I calculated the partial derivative of z with respect to x and y and set them to zero.
The problem is I got a complicated system of equations that was hard to solve.
This question was before the part about Lagrange multipliers, so is there another way to solve it.
I also noticed that the two equations were symmetric, so would that imply that x and y are interchangeable and might be equal?