How to calculate the dimensions of a parcel?

Question

Mathematics

Hello.
There are two products. The first with dimensions A1, B1, C1, and the second A2, B2, C2. I need to calculate and transfer the total dimensions of two products. It would be easier for me to calculate the volumes of each product and add them up. But the system requires me to pass exactly the length, width and height.
What is the formula to calculate them?

Answer 1

Obviously, the answer will depend on how you stack them. There aren't many combinations. If the box A is fixed in a certain coordinate system with the X, Y, Z axes, then there are several ways to lay B:
- On top of A (higher in the Z direction)
- To the right of A (in the X axis direction)
- In front of A (along the direction of the Y axis)
Options such as below, to the left, behind A in the sense of boxing do not carry any difference.
For each of the three options, you can calculate the box described around the first two. For example, for the first case we have: max(A1, B1), max(A2, B2), sum(A3, B3).
Of the three combinations, you can choose the one where the volume is the smallest, that is, the packaging is denser.

Answer 2

How to calculate the parcel size?

Answer 3

Put one on top of the other. The length and width of the final design is the maximum of each dimension of each item. Height - sum.
Or do you need to pack optimally?