# Math

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?

1. 👍 0
2. 👎 0
3. 👁 158
1. Let squares of size x" be cut from the corners.

Volume of (open) box
=V(x)
=height*length*width
=x(11-2x)(7-2x)
=4x^3-36x^2+77x

For maximum (or minimum), equate derivative to zero:
dV(x)/dx = 12x²-72x+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 cut-outs 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 = 24x-72 = -38.6 <0 OK.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Algebra

A rectangular piece of cardboard is 15 inches longer than it is wide. If 5 inches are cut from each corner, and the remaining fold up to form a box,the volume of the box is 1250 cubic inches. Find the dimensions of the piece of

asked by Alberto on May 12, 2014
2. ### calculus optimization problem

by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 30 inches long and 14 inches wide find the dimensions of the

asked by sasha on April 3, 2013
3. ### Math

a rectangular piece of cardboard is twice as long as it is wide . from each of its for corners, a square piece 3 inches on a side cut out. the flaps at each corner are then turned up to form an open box. if the volume of the box

asked by Anonymous on August 26, 2015
4. ### Algebra

A box with no top is to be constructed from a piece of cardboard whose length measures 6 inch more than its width. The box is to be formed by cutting squares that measure 2 inches on each side from the four corners an then folding

asked by T H on April 5, 2013
5. ### math

a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2-in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard.

asked by Amy on February 15, 2011
6. ### Geometry

A box of cereal measures 8 inches high and 2 inches deep. If all surfaces are made of cardboard and the total amount of overlapping cardboard in the box is 7 square inches, how much cardboard is used to make the cereal box?

asked by Sholanda on May 29, 2012
7. ### Geometry

A square piece of cardboard, 24 inches by 24 inches, is to be made into an open box by cutting out each of the four corners. Each side of the box will then be folded up. Find the maximum volume that the box can hold.

asked by Tom on November 13, 2014
8. ### Math HELP!!

Chuck needs to cut a piece of cardboard for an art project at school. He has four pieces of cardboard that he can cut from: 6 inches, 5 inches, 7 inches, and 3 inches. If the length of the cardboard he needs is √35 inches, which

asked by lily on November 2, 2016
9. ### Math

Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

asked by Jacinta on June 25, 2009
10. ### Math

Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

asked by Jamie on June 23, 2009

More Similar Questions