maximum dimensions-very interesting!!

[joejo]

hey guys....i have another question...i posted my answer right below it...does it look right guys?! I hope so! Thanks in advance

You are to design a container box by cutting out the four corners of a square cardboard sheet that is 1600cm^2 in area. The box must have a square base and an open top. Determine the dimensions of the box that give maximum value.

The side of the square cardboard is 40 cm. Let side of corner square is a cm. The volume of the box V = (40-2a)2.a cm3 , For max volume we have dV/da = 0 implies (20-3a)(20-a) = 0, i.e., a = 20, a = 20/3. But when a = 20, V = 0. So to maximize the volume a = 20/3. So the base of is a square of side 80/3 cm and height = 20/3 cm.

Sorry not good with latex...

[Galileo]

Yes, that looks good. It's intuitively clear that a=20/3 should be a maximum (there must be 'some' maximum between a=0 and a=20), but for completeness you might want to show it is a maximum indeed (depends on your teacher).

[joejo]

thanks for your help!