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
Answer This Question
Related Questions
 math  open top rectangular box made from 35 x 35 inch piece of sheet metal by ...
 math  a rectangular sheet of cardboard 4m by 2m is used to make an open box by ...
 Calculus  A square sheet of cardboard with a side 16 inches is used to make an ...
 calculus  An open box is to be made from a 21 ft by 56 ft rectangular piece of ...
 Calculus  A SHEET OF CARDBOARD 180 INCHES SQUARE IS USED to make an open box by...
 calculus  an open box is to be made from a piece of metal 16 by 30 inches by ...
 Math  A box with a rectangular base and no top is to be made from a 9 inch by ...
 Math Wrod Problem  1. A long strip of copper 8 inches wide is to be made into a...
 Calculus  A box with an open top is to be made from a square piece of cardboard...
 College Math  An opentopped rectangular box is to be constructed from a 24 ...
More Related Questions