Container Packing (SQA National 5 Applications of Mathematics): Revision Note

Container packing

What is the container packing problem?

• You will be given:

  • a container with dimensions

  • a box with dimensions

• You need to find the maximum number of boxes that fit in the container

• All boxes need to be aligned in the same direction

• Consider the direction orientations for the boxes

  • There are 6 different orientations

  • However, there will be restrictions in a question to reduce this to 2 or 3

How do I find the number of boxes that will fit in a container using a given orientation?

• Change any necessary lengths so that they are all in the same units

• STEP 1
  Find how many boxes you can fit on top of each other

  • Divide the height of the container by the height of a box

  • Round down to the next whole number

• STEP 2
  Find how many boxes you can fit on next to each other in one direction

  • Divide the width of the container by the width of a box

  • Round down to the next whole number

• STEP 3
  Find how many boxes you can fit on next to each other in the other direction

  • Divide the breadth of the container by the breadth of a box

  • Round down to the next whole number

• STEP 4
  Multiply the number of boxes in the three directions together

What are the options if the boxes need to be packed upright?

• There are two orientations if the boxes need to be packed upright

• It is easier to visualise these using a bird's eye view

• The two options are:

  • the longer side of the box sits alongside the longer side of the container

  • the shorter side of the box sits alongside the longer side of the container

What are the options if the boxes have a square base?

• There are three orientations if the boxes have a square base

  • Two of the lengths are equal and the third is different

• The three options are:

  • the third length is used as the height of the box

  • the third length is used as the width of the box

  • the third length is used as the breadth of the box