Solve Lowest Cost Cuboid Volume Problem - Philipp

[philipp2020]

hi

today i have another problem where i am not sure

Here is the question:

A cuboid, made of an square ground and which is open on the top should have the volume of 2 squaremeters. The costs for the material of the 4 sides have the double price as for the material of the square ground. Search for the cuboid with the lowest cost...

So I formed 2 equations for this problem:

1: V = x^2 * h -----> 2 = x^2 * h --->

2: 2 x^2 = 4 * x* h ------> h = 1/2 x

At the end I received a result for a length of 2 meter for square side's bottom and a hight of 0.5 meter. The result seems to be right. But I don't know if the way I solved it afterwards is right or not.

Can somebody show me the right forms for the way to the result?

Thanks very much

Philipp

 

[BobG]

Your first equation is good, but you can rearrange it to solve for h. This will allow you to make a substitution in your second equation so you'll only be dealing with one variable.

For your second equation, you need the surface area, which is:

$$x^2 + 4xh$$

Since the side material is twice as expensive as the bottom material, the cost of the surface area material will be the cost of the bottom material (unimportant) times this:

$$x^2 + 2 * 4xh$$

Substitute for h (from your first equation).

Take the derivative.

Set the derivative equal to zero.

You will wind up with the same answer you gave, although you didn't really explain how you got there.

 

[philipp2020]

and then out of x^2 + 16 *1/x

derivate:

2x - 16x^-2 = 0

An then i try to find the 0 points of this equation with a discriminant?

But how can I if there is a minus exponation. How can I find the minimum now?

 

[philipp2020]

ok thanks i found the way. Just multiply with x^2 and there it is

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