An open rectangular box having a volume of is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x by y by z. Then, xyz = 108 and the amount of material used is given by S = xy + 2yz + 2xz. Show that Minimize f(x, y)
A) x = 1; y = 1; z = 2
B) x = 2; y = 2; z = 1
C) x = 2; y = 1; z = 1
D) x = 2; y = 1; z = 2

Question

An open rectangular box having a volume of  is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x by y by z. Then, xyz = 108 and the amount of material used is given by S = xy + 2yz + 2xz. Show that  Minimize f(x, y)
A) x = 1; y = 1; z = 2 
B) x = 2; y = 2; z = 1 
C) x = 2; y = 1; z = 1 
D) x = 2; y = 1; z = 2

Quizplus · Accepted Answer

The Answer of An open rectangular box having a volume of  is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x by y by z. Then, xyz = 108 and the amount of material used is given by S = xy + 2yz + 2xz. Show that  Minimize f(x, y)
A) x = 1; y = 1; z = 2 
B) x = 2; y = 2; z = 1 
C) x = 2; y = 1; z = 1 
D) x = 2; y = 1; z = 2

An Open Rectangular Box Having a Volume of Is