SOLUTION: A manufacture wants to design an open box that has a square base and surface are of 108 square inches,.What dimensions will produce box with a max volume.

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Question 1114500: A manufacture wants to design an open box that has a square base and surface are of 108 square inches,.What dimensions will produce box with a max volume.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Base of x by x;
height of y;

Surface Area, x%5E2%2B4xy=108
Volume, x%5E2%2Ay

4xy=108-x%5E2
y=%28108-x%5E2%29%2F%284x%29


v=x%5E2%2Ay
v=x%5E2%28108-x%5E2%29%2F%284x%29
v=x%28108-x%5E2%29%2F4
v=%281%2F4%29%28108x-x%5E3%29
From here you could either try a graphing tool, or find derivative to help identify a maximum volume for the box. This is to get this x value from which you can then find the corresponding y value.