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LOGO-L> Solving a Max Problem Using Logo



Hi,

To solve min-max problems we need usually calculus. But if we have Logo,  we can solve this sort of problems, with much younger students.

Here's a sample problem:

We create an open box from a cardboard square, with side length of 30 units. To do this, we cut from each of its corners a square of x length units -
all squares are the same - and then fold the cardboard along the cut lines (in the attached drawing, the to-be-removed squares are darkened, and the
folding lines are drawn in red):

After the necessary folding we get a coverless box with a square base:
 

The problem is:

What should x be, so that the volume of the box be maximal?

Before going further, we might ask: Are there aa all solutions? Are there several solutions? Is there only one solution?

So I wrote a short Logo program, to demonstrate the change of the volume with the change of x. [ We note, that x can not be more than 15 (why?) ]

Here's my program's output:
 
We  see that at first the volume increases with x, until it reaches its maximal value, and that  there's exactly one max point (math teacher call this point  "an
extremum").

All we have now to do is to write a Logo program that calculates the numeric value of x, which gives the maximal volume.

One might want to do the programming job by himself, so I leave it for the interested.

Addendum: In calculus it's shown, that the side of our x is one sixth of the square side. So, the solution in our case is:

    x = 30 / 6 = 5

Regards...

[[Yehuda]]

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