A closed rectangular box with square ends is to be designed so that the surface area of the box is minimized. [Note: Surface area = 2 $x ^ { 2 }$ + 4xy.] It is required that the volume be 32 cubic inches. Which of the following is the Lagrange function F(x, y, λ) for this problem?
A) 2 $x ^ { 2 }$ + 4xy + λ(32)
B) ( $x ^ { 2 }$ y - 32) + λ(2 $x ^ { 2 }$ + 4xy)
C) 2 $x ^ { 2 }$ + 4xy + λ( $x ^ { 2 }$ y - 32)
D) $x ^ { 2 }$ y + λ(2 $x ^ { 2 }$ + 4xy - 32)
E) none of these

Question

A closed rectangular box with square ends is to be designed so that the surface area of the box is minimized. [Note: Surface area = 2 $x ^ { 2 }$ + 4xy.] It is required that the volume be 32 cubic inches. Which of the following is the Lagrange function F(x, y, λ) for this problem? 
A) 2 $x ^ { 2 }$ + 4xy + λ(32) 
B) ( $x ^ { 2 }$ y - 32) + λ(2 $x ^ { 2 }$ + 4xy) 
C) 2 $x ^ { 2 }$ + 4xy + λ( $x ^ { 2 }$ y - 32) 
D) $x ^ { 2 }$ y + λ(2 $x ^ { 2 }$ + 4xy - 32) 
E) none of these

Quizplus · Accepted Answer

The Answer of A closed rectangular box with square ends is to be designed so that the surface area of the box is minimized. [Note: Surface area = 2 $x ^ { 2 }$ + 4xy.] It is required that the volume be 32 cubic inches. Which of the following is the Lagrange function F(x, y, λ) for this problem? 
A) 2 $x ^ { 2 }$ + 4xy + λ(32) 
B) ( $x ^ { 2 }$ y - 32) + λ(2 $x ^ { 2 }$ + 4xy) 
C) 2 $x ^ { 2 }$ + 4xy + λ( $x ^ { 2 }$ y - 32) 
D) $x ^ { 2 }$ y + λ(2 $x ^ { 2 }$ + 4xy - 32) 
E) none of these

A Closed Rectangular Box with Square Ends Is to Be x2x ^ { 2 }x2

A Closed Rectangular Box with Square Ends Is to Be $x ^ { 2 }$