Hi everyone.
Boy do I have a fun one for you today!
A peice of sheet metal has area.
Create an open top box with a quare bottom that has the largest
possible volume. Did not get very far on this one. I have no idea how
to solve this problem. :P
Hi
If it were the case, I think the problem couldn't be solved, there would be too many conditions. (unless it is useless information )
Lets call the height of the box and its width.
This gives a relation between and (the area of the box is the sum of the area of each side and has to be )
Then, you should know what is the volume of the box in function of and and, thanks to what you've done before, you can rewrite it as a function of only one variable. (say )
This gives a condition on the derivative of the volume which gives us and from which we get .that has the largest possible volume.