A rectangular box of length x, width y, and height z has a surface are of 700 cm². Set- up the Lagrange equations that will give the dimension of the box that will maximize the volume of the box. O yz = A (2y + 2z+ 700) xz = X(2x + 2x + 700) xy = X(2x + 2y + 700) 2xy + 2yz + 2xz = 700 yz = 2X (y+z) x2 = 2X(x + 2) xy=2\(2 +y) xy+yz+xz = 350 yz = A (2y + 2z - 700) xz = X(2x + 2x - 700) xy = X(2x + 2y - 700) 2xy + 2yz + 2xz = 700 yz = (y +z = 350) xz = x(x + z- 350) xy = x(x + y − 350) 2xy + 2yz + 2xz = 350 о O O O All of the above O None of the above
A rectangular box of length x, width y, and height z has a surface are of 700 cm². Set- up the Lagrange equations that will give the dimension of the box that will maximize the volume of the box. O yz = A (2y + 2z+ 700) xz = X(2x + 2x + 700) xy = X(2x + 2y + 700) 2xy + 2yz + 2xz = 700 yz = 2X (y+z) x2 = 2X(x + 2) xy=2\(2 +y) xy+yz+xz = 350 yz = A (2y + 2z - 700) xz = X(2x + 2x - 700) xy = X(2x + 2y - 700) 2xy + 2yz + 2xz = 700 yz = (y +z = 350) xz = x(x + z- 350) xy = x(x + y − 350) 2xy + 2yz + 2xz = 350 о O O O All of the above O None of the above
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.1: Parabolas
Problem 36E
Related questions
Question
![A rectangular box of length x, width Y, and
height z has a surface are of 700 cm². Set-
up the Lagrange equations that will give
the dimension of the box that will
maximize the volume of the box.
O
yz = A (2y + 2x + 700)
x2 = A(2x + 2x + 700)
xy = A(2x + 2y + 700)
2xy + 2yz + 2xz = 700
yz
= 2X (y+z)
xz = 2x(x + 2)
xy=2X(x + y)
xy+yz + xz = 350
yz = λ (2y + 2z - 700)
X(2x + 2x - 700)
XZ =
xy =
X(2x + 2y - 700)
2xy +
2yz + 2xz = 700
yz =
(y +z - 350)
xz =
x(x + z- 350)
xy = x(x + y − 350)
2xy + 2yz + 2xz = 350
O
O
O
O All of the above
O None of the above](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99b0b82e-7764-4422-9616-bb186733feb7%2F8377b12d-d7ae-4b12-8c24-929284bf20d9%2Fcrsxmg_processed.png&w=3840&q=75)
Transcribed Image Text:A rectangular box of length x, width Y, and
height z has a surface are of 700 cm². Set-
up the Lagrange equations that will give
the dimension of the box that will
maximize the volume of the box.
O
yz = A (2y + 2x + 700)
x2 = A(2x + 2x + 700)
xy = A(2x + 2y + 700)
2xy + 2yz + 2xz = 700
yz
= 2X (y+z)
xz = 2x(x + 2)
xy=2X(x + y)
xy+yz + xz = 350
yz = λ (2y + 2z - 700)
X(2x + 2x - 700)
XZ =
xy =
X(2x + 2y - 700)
2xy +
2yz + 2xz = 700
yz =
(y +z - 350)
xz =
x(x + z- 350)
xy = x(x + y − 350)
2xy + 2yz + 2xz = 350
O
O
O
O All of the above
O None of the above
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