Wednesday
June 19, 2013

# Homework Help: math

Posted by ibranian on Tuesday, August 7, 2012 at 1:31pm.

Your iron works has been contracted to design and build a 500-ft3 square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding half-inch-thick stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible. What dimensions do you tell the shop to use?

• math - Reiny, Tuesday, August 7, 2012 at 2:10pm

clearly the weight of the box is a function of the material used, which in turn depends on the surface area of the sheet metal used.
So we want a minimum surface area.
let each side of the base be x ft, and let the height be y ft.
Area = x^2 + 4xy
but x^2 y = 500
y = 500/x^2

area = x^2 + 4x(500/x^2) = x^2 + 2000/x
d(area)/dx = 2x -2000/x^2 = 0 for a min of area
2x = 2000/x^2
x^3 = 1000
x = 10 , then y = 500/10^2 = 5

the box should have a base of 10 ft by 10 ft, and a height of 5 ft.

Related Questions

Calculus AB/AP - A tank with a rectangular base and rectangular sides is to be ...
calculus - A tank with a rectangular base and rectangular sides is to be open at...
math - an open steel tank measures 2m by 2.5m by 3m.It holds 7500 ml of water....
math - An open steel tank measures 2m by 2.5m by 3m.It holds 7500 ml of water. ...
Physics - Assume you construct a new water tower for a town water supply. Assume...
Calculus (optimization problem) - A cyclinderical tank with no top is to be ...
Chemistry - A Balloon Time® tank holds 15% excess capacity to fill 50 helium...
calculus - Find the dimensions of the largest open-top storage bin with a square...
math-optimal diameterand height - A cylindrical oil-storage tank is to be ...
Math Nightmare - I need help The design of a new airplane requires a gasoline ...