Posted by Anonymous on .
A Candy box is made from a piece of cardboard that meaasures 11 by 7 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume?

Math 
MathMate,
Let squares of size x" be cut from the corners.
Volume of (open) box
=V(x)
=height*length*width
=x(112x)(72x)
=4x^336x^2+77x
For maximum (or minimum), equate derivative to zero:
dV(x)/dx = 12x²72x+77=0
Solve for x to get
x=3±(√93)/6
=1.39 or 4.61 (approximately)
4.61 is clearly not a feasible solution (because 2*4.61 > 7") and will be rejected.
So the cutouts will be squares of 1.39" (approximately).
Now verify that the solution so obtained is a maximum by ensuring that d²V(x)/dx² < 0:
d²V(x)/dx² = 24x72 = 38.6 <0 OK.