Posted by NONO on Wednesday, December 7, 2011 at 11:53am.
An open box is to be made from a 10ft by 14ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and folding up the sides. what size squares should be cut to obtain a box with largest possible volume?

Math  Reiny, Wednesday, December 7, 2011 at 12:19pm
let each side of the cutoutsquares be x ft
so the box will be 102x y 142x by x
V = x(102x)(142x)
= x(140 48x + 4x^2)
= 140x  48x^2 + 4x^3
d(V)/dx = 140  96x + 12x^2 = 0 for a max of V
3x^2  24x + 35 = 0
x = (24 ± √156)/6
= appr. 1.92 or 6.08 , but obviously 102x > 0 > x > 5
cut out should be 1.92 ft by 1.92 ft
check my arithmetic