Optimization - open top box

[q_fruit]

Straight from my textbook:

Your iron works has constracted to design and build a 500 ft^3, square-based, open-top, rectangular steel holding tank for a paper company. The tank is to be made by welding 1/2 in.-thick stainless steele 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 weigh as little as possible. What dimensions do you tell the shop to use?

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I'm guessing the 1/2 in.-thick part of the question doesn't really matter. I don't know how to find the dimensions of the V (lwh) just knowing it equals 500..and have it contain only 1 variable.

I'm very calculus-challenged..please help! thank u.

 

[Guest]

The mass limit is another way of saying the area needs to be at the min.

Vol = x. y where these are each sides (x is the base, y is the height)

500 = x . x . z

y =500/(x . x)

Area = x.x + 4x.y

now sub in the y = 500(x^2) into the above equation

You now have an equation with one variable, do dA/dx of this, solve for 0, and confirm it is a min .

Over to you for a go