Answer: A cardboard box without a lid is to have a volume of 32,000 cubic cm. Find the dimensions that minimize the amount of cardboard used
. ans: base 40 x 40, height = 20
Solution:
The typical box might look like the one below
where . In addition we have xyz = 32000 ,so we need to minimize .
We have,
From the geometry of the problem so y = x. So or x = 40.
Finally, y = x = 40 and z = 32000/(xy)=20.