Question and answer
You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. Which of the
following dimensions will give you the greatest volume? A. 12 in. by 22 in. by 4 in. B. 10 in. by 20 in. by 5 in. C. 14 in. by 24 in. by 2 in. D. 10 in. by 24 in. by 6 in
You cut square corners with side lengths that are whole numbers from a piece of cardboard with dimensions 20 inches by 30 inches. You then fold the cardboard to create a box with no lid. 12 in. by 22 in. [ by 4 in will give you the greatest volume. ***Length of box base: 20 - 2x Width of box base: 30 - 2x Height of box: x Volume of box: V = x(20 - 2x)(30 - 2x) V = x(600 - 40x - 60x +
4x^2) V = x(600 - 100x + 4x^2) V = 600x - 100x^2 + 4x^3 dV/dx = 600 - 200x + 12x^2 Set that to zero: 12x^2 - 200x + 600 = 0 x = (-(-200) +/- sqrt((-200)^2 - 4(12)(600))) / (2*12) x = (200 +/- sqrt(40000 - 28800)) / 24 x = (200 +/- sqrt(11200)) / 24 x = (200 +/- sqrt(11200)) / 24 x =~ 12.74 or 3.92 Since you want whole numbers, x = 13 or 4 If x = 13, V = -312, but a negative number doesn't make sense, so we'll ignore that If x = 4, V = 1056, so that's the maximum volume The dimensions are: Length of box base: 12 Width of box base: 22 Height of box: 4 ]
Expert answered|emdjay23|Points 3026|
Question
Asked 12/22/2013 12:21:58 PM
0 Answers/Comments
Get an answer
New answers
Rating

There are no new answers.

Comments

There are no comments.

Add an answer or comment
Log in or sign up first.
25,343,695 questions answered
Popular Conversations
8!
Weegy: hello what is your question? User: 0!=0 Weegy: The answer is zero. The property is identity property of ...
5/26/2016 2:58:30 PM| 2 Answers
Weegy Stuff
S
Points 662 [Total 662] Ratings 10 Comments 542 Invitations 2 Offline
S
Points 649 [Total 649] Ratings 12 Comments 529 Invitations 0 Offline
S
Points 592 [Total 592] Ratings 0 Comments 592 Invitations 0 Offline
S
1
L
L
P
R
P
L
P
P
R
Points 287 [Total 12539] Ratings 2 Comments 267 Invitations 0 Offline
S
L
P
P
P
Points 166 [Total 3543] Ratings 0 Comments 166 Invitations 0 Offline
S
Points 38 [Total 107] Ratings 0 Comments 38 Invitations 0 Offline
S
Points 12 [Total 12] Ratings 1 Comments 2 Invitations 0 Offline
S
Points 10 [Total 10] Ratings 1 Comments 0 Invitations 0 Offline
S
Points 4 [Total 4] Ratings 0 Comments 4 Invitations 0 Offline
S
Points 3 [Total 3] Ratings 0 Comments 3 Invitations 0 Offline
* Excludes moderators and previous
winners (Include)
Home | Contact | Blog | About | Terms | Privacy | © Purple Inc.