If 2 700 cm2 of material is available to make a rectangular

If 2. 700 cm2 of material is available to make a rectangular box with a square base and an open top, find the largest possible volume of the box. Justify why your answer is absolute maximum.

Solution

\\(lbh = V\\) \\(lb + lh + bh = 2700\\) \\(\\frac{1}{h} +\\frac{1}{b} +\\frac{1}{l} = 2700/V\\) Using these constraints we get \\(l = b =h = 30cm\\)