Asked by Marissa
A rectangular tank with a square base, an open top, and a volume of 4,000 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
I'm not understanding how to get started and find the optimization function (for any of these problems).
I'm not understanding how to get started and find the optimization function (for any of these problems).
Answers
Answered by
Damon
side = x
height = y
volume = x^2y = 4000 so y = 4000/x^2
area = A = x^2 + 4 x y
A = x^2 + 4 x (4000/x^2)
A = x^2 + 16000/x
min or max when dA/dx = 0
0 = 2x -16000/x^2
16000 = 2 x^3
x^3 = 16000
x = 25.2
y = 4000/x^2 = 6.3
height = y
volume = x^2y = 4000 so y = 4000/x^2
area = A = x^2 + 4 x y
A = x^2 + 4 x (4000/x^2)
A = x^2 + 16000/x
min or max when dA/dx = 0
0 = 2x -16000/x^2
16000 = 2 x^3
x^3 = 16000
x = 25.2
y = 4000/x^2 = 6.3
There are no AI answers yet. The ability to request AI answers is coming soon!