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There are many volume-of-a-box questions. I like this one, simpler than what the OP cites:

Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.

The rectangle might be specialized to a square, as below. See also The Math Forum.

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          [![BoxVol][1]][1]
          ^{(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)}

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In response to [@RoryDaulton](https://matheducators.stackexchange.com/questions/14692/list-of-realistic-extremum-problems#comment37319_14692), here is the box problem to which the OP @Student points: [![BoxFlaps][2]][2]

There are many volume-of-a-box questions. I like this one, simpler than what the OP cites:

Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.

The rectangle might be specialized to a square, as below. See also The Math Forum.

---

          [![BoxVol][1]][1]
          ^{(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)}

---

---

In response to [@RoryDaulton](https://matheducators.stackexchange.com/questions/14692/list-of-realistic-extremum-problems#comment37319_14692), here is the box problem to which the OP @Student points: [![BoxFlaps][2]][2]

There are many volume-of-a-box questions. I like this one, simpler than what the OP cites:

Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.

The rectangle might be specialized to a square, as below. See also The Math Forum.

---

          [![BoxVol][1]][1]
          ^{(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)}

---

---

In response to @RoryDaulton, here is the box problem to which the OP @Student points: [![BoxFlaps][2]][2]

There are many volume-of-a-box questions. I like this one, simpler than what the OP cites:

Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.

The rectangle might be specialized to a square, as below. See also The Math Forum.

---

          [![BoxVol][1]][1]
          ^{(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)}

---

---

In response to [@RoryDaulton](https://matheducators.stackexchange.com/questions/14692/list-of-realistic-extremum-problems#comment37319_14692), here is the box problem to which the OP @Student points: [![BoxFlaps][2]][2]

There are many volume-of-a-box questions. I like this one, simpler than what you cite:

Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.

The rectangle might be specialized to a square, as below. See also The Math Forum.

---

          [![BoxVol][1]][1]
          ^{(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)}

---

There are many volume-of-a-box questions. I like this one, simpler than what the OP cites:

Given a rectangle, cut out squares from the corners so you can fold it up to a box, without a top, of maximal volume.

The rectangle might be specialized to a square, as below. See also The Math Forum.

---

          [![BoxVol][1]][1]
          ^{(Image from [patrickJMT](https://www.youtube.com/watch?v=_oS_LjKse38) YouTube video.)}  

---

---

In response to @RoryDaulton, here is the box problem to which the OP @Student points: [![BoxFlaps][2]][2]