# Thread: Optimization problem

1. ## Optimization problem (still NOT solved)

This problem does not make sense to me, partly because I don't know what they mean by cross section area in this case.

A trough is made from a rectangular strip of sheet metal, 50 cm wide, by bending up at right angles a strip, x cm wide, along two sides. For what value of x is the cross-section area a maximum?

2. i think the answer is 12.5 but I'm not positive.

3. I don't care about the answer, I care about understanding. Thanks.

4. I know it is against the rules to bump, but my question is still not solved. Someone please help?

5. Describe the area of the cross-section in terms of x.

The area is $A(x) = x(50 - 2x)$. Do you know how to maximize this function?

6. Originally Posted by icemanfan
Describe the area of the cross-section in terms of x.

The area is $A(x) = x(50 - 2x)$. Do you know how to maximize this function?
I know how to do this, but I don't understand what the cross section area in this question meant. I only dealt with cross section area in volume with integration problems, so I'm stuck here, feeling stupid.

Do you mind explaining how did you get $A(x)=x(50-2x)$? Thanks.

7. Originally Posted by chengbin
I know how to do this, but I don't understand what the cross section area in this question meant. I only dealt with cross section area in volume with integration problems, so I'm stuck here, feeling stupid.

Do you mind explaining how did you get $A(x)=x(50-2x)$? Thanks.
Certainly. The metal sheet is 50 cm wide, and it is arbitrarily long. If you turn the sheet so that the 50 cm wide side is facing you, and then fold up a length x cm of the sheet on both sides, each side that you folded up has a length of x cm, which was part of the original 50 cm. The width of the sheet still touching the ground is 50 cm minus the lengths of the folded up parts, which is x + x or 2x, so this width is 50 - 2x. If you folded up the sides at ninety degree angles, the folded up parts and the part touching the ground form a rectangle with the given area.

8. In this problem, you are not given the other length of the rectangular
sheet of metal, so all that can be assumed is that, the two sides be bent up from both ends of the 50cm width.

Therefore the only cross-section analysable is the vertical cross-section
of one side view.

There is also a plan-view cross-section, but we don't have the 2nd length of the rectangular sheet, and a perpendicular side view with a 3rd cross-section.