最大化矩形框的音量 [英] Maximize the volume of the rectangular box

问题描述

Johnny需要为他的物理课项目制作一个矩形框。他买了P厘米的电线和S cm2的特殊纸。他想用所有的电线（12个边缘）和纸张（6个边）制作盒子。



什么是最大的音量约翰尼可以制作的盒子吗？



我尝试过：



矩形的表面积是2（wl + hl + hw）

和p = 4w + 4h + 4l

我如何使用2个方程来找到3个变量！ ！

Johnny needs to make a rectangular box for his physics class project. He has bought P cm of wire and S cm2 of special paper. He would like to use all the wire (for the 12 edges) and paper (for the 6 sides) to make the box.

What is the largest volume of the box that Johnny can make?

What I have tried:

the surface area of the rectangle is 2(wl+hl+hw)
and p = 4w + 4h +4l
how do i use 2 equations to find 3 variable !!

推荐答案

看起来没有人发现这个问题的制定中的错误，这会使问题错误地构成。



P cm of wire非常有意义，但Scm²却没有。这是因为解决方案取决于要使用的纸张的形状。甚至没有指定纸张的形状;例如，它从未说过这是一个矩形。例如，输入条件是声明纸张是正方形，这个问题可以正确制定。但是没有类似的东西可以制定。



正确制定问题的另一种方法是：假设人们可以购买一张无限大小和形状的纸张。纸店。一个人应该首先计算最佳盒子大小，假设纸张总面积应为Scm²，然后才能在商店中订购所需形状的纸张。也许这就是暗示，但我无法确定。未能制定形状应该是一个错误的逻辑错误。



另一个小问题是：没有规定电线应保持单件或可以削减。严格来说，这也不是很明显。它只会产生两个不同的问题;每个都可以单独解决。



（顺便说一下，没有矩形框这样的术语。可能应该假设这是cuboid ，但仅仅因为很难以任何不同的方式解释它。这虽然是一个小问题。）



唯一正确的解决办法是将问题解决为错误配方。



最后，我想注意证明一些解决方案是没有提到的极值。没有这样的证据，这些问题几乎没有价值。顺便说一下，这个问题根本与编程无关。一些数学问题也可以被认为是算法问题，因此也是相关的，但不是这个问题。

-SA

It looks like no one spotted the mistake in the formulation of this problem, which makes the problem incorrectly posed.

"P cm of wire" makes perfect sense, but "S cm²" doesn't. This is because the solution depends on the shape of the piece of paper to be used. Even the shape of the piece of paper is not specified; for example, it's never said that this is a rectangle. It, for example, the input condition was a statement that there the piece of paper was a square, the problem would be correctly formulated. But nothing like that is formulated.

Another way to formulate the problem correctly would be this: suppose that one could buy a piece of paper of unlimited size and shape in a paper shop. A person is supposed to first calculate the "optimal" box size, assuming that the total paper surface should be S cm² and only then order the piece of paper of the required shape in the shop. Maybe this is what was implied, but I could not be sure. The failure to formulate what a shape should be is just the bad logical mistake.

Another little problem is: it is not specified of the wire should remain in one piece or can be cut. Strictly speaking, this is also not obvious. It would just make two different problems; each can be solved separately.

(By the way, there is no such term as "rectangular box". It probably should assume that this is "cuboid", but only because it's hard to interpret it in any different way. This is a minor problem though.)

The only correct solution would be to dismiss the problem as incorrectly formulated.

Finally, I would like to note that the proof of that some solution is the extremum is not mentioned. Without such proof, such problems have little value. By the way, the problem has nothing to do with programming at all. Some mathematical problems could be considered also algorithmic ones and hence relevant, but not this one.

—SA

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'Assuming you want to make a box that has each side 4cm long
      'and you want to know how many paper square and wire you need for.
      BOX_SIDE = 4cm
      P = ((4 * 4) * 6) = 96cm square paper
      W = (4*12) = 48 cm Long wire

      'Assuming you want to know how long has to be each side of the box by a 150 cm square paper
      P = 150 cm square
      SIDE = √((P / 6)) 'square root of (P/6)

      'Assuming you want to know how long has to be each side of the box by a 80 cm wire available
      W = 80 cm Long
    SIDE = (W / 12)

      'Assuming you want to make the biggest perfect possible box either by available paper or wire
      P = 140 'cm2
      W = 70 ' cm long
      'we have to work here with conditions, either paper or wire will be left over
      'you can build a maximum large box with;
      'check what can do the paper
      side_by_paper = √(P/6) '=4.83 cm
      'check what can do the wire
      side_by_wire = (W / 12) '=5,83 cm
      'select now the smallest possible (minimum) of the two
      max_side_length = Math.Min(side_by_paper, side_by_wire) ' =4.83
      'you can build a maximum large box with;

BOX_CUBIC_cm3 = (max_side_length)3
'That is a BOX with each side (4.83cm * 4.83cm * 4.83cm) = 112.67 cm3
'where each surface of the BOX has a square of 23.32 cm2
This time there was less paper than wire to build your box,
so 70- (4.83*12) = 12.04 cm wire left over...

$ b $b√s quare root示例：√144= 12，√4= 2

Pcm3 =√（P / 6）^ 3 [纸方形立方体纸]

W =√（P）* 12 [来自可用纸方的电线]

P =（（（W / 12）*（W / 12））* 6）[可用电线的纸张方形] < br $>
P =（（SIDE * SIDE）* 6）[特定边长的纸张方格]

SIDE =√（P / 6）[可用纸张方面的一面]

SIDE =（W / 12）[可用电线的一侧]

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