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.
23,849,169 questions answered
Weegy Stuff
S
Points 191 [Total 588] Ratings 0 Comments 191 Invitations 0 Offline
S
P
P
Points 142 [Total 949] Ratings 0 Comments 142 Invitations 0 Offline
S
1
L
L
P
R
P
L
P
Points 106 [Total 11279] Ratings 0 Comments 106 Invitations 0 Offline
S
L
P
Points 46 [Total 2114] Ratings 0 Comments 46 Invitations 0 Offline
S
Points 13 [Total 23] Ratings 0 Comments 13 Invitations 0 Offline
S
Points 4 [Total 904] Ratings 0 Comments 4 Invitations 0 Offline
S
Points 4 [Total 4] Ratings 0 Comments 4 Invitations 0 Offline
S
R
Points 2 [Total 438] Ratings 0 Comments 2 Invitations 0 Offline
S
Points 2 [Total 2] Ratings 0 Comments 2 Invitations 0 Offline
S
Points 1 [Total 2] Ratings 0 Comments 1 Invitations 0 Offline
* Excludes moderators and previous
winners (Include)