Containers

1
Containers

• An Investigation

2

• Containers
• Consider the container
• It is required to design a box which satisfies
  the following requirements-
• a) The box is to hold 2000cm3 (2 litres)
• b) The length of the box is to be two times
  the
• breadth of the box.
• c) The amount of cardboard needed to make
  the
• box is to be a minimum.

3

• Steps-
• 1. Use the fact that V LBH to show that
• 2 Show that the total area of cardboard
• needed is
• 3. Put into Y1 and use
  the TABLE
• function on the graphic calculator to obtain the
  solution.

4

• Table 1
• Complete the table shown
• to show your results.

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• You can see from the table that the minimum is
  somewhere between x 8 and x 10.
• So we now form another table with x going up in
  steps of 0.2 say.
• On your calculator set TblStart to 8 and ?Tbl to
  0.2 and then complete the Table 2 on the next
  slide.

6

• Table 2
• Why have we
• stopped this
• Table at 9.6?

7

• Make up a third table starting at ? and going
  up in steps of 0.1 to obtain the final value for
  x which will give the minimum area of cardboard.
• Now that you have this value of x, draw a box
  like the one below and mark on the box the
  dimensions which the box would have for this
  minimum area.

8

• Note
• A company using this box for packaging goods,
  would produce millions of these boxes and the
  cost of producing them would be a minimum because
  each box uses the smallest amount of cardboard
  and satisfies the other conditions stated
  initially in the problem.

9

• Container Examples
• (Using the graphic calculator Table function)
• 1. The container is to hold a volume of 800cm3.
• The length is to be five times the breadth.
• The area of cardboard needed to make the
  container is to be a minimum.
• Find x, then draw the container.

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• Ex2. Design a container to satisfy the following
  requirements.
• The container is to hold a volume of 1200cm3.
• The container has a square base.
• The area of cardboard needed to make the
  container is to be a minimum.

11

• Ex3. Design the container below
• The container is to hold a volume of 1500cm3.
• The length is to be two times the breadth.
• The area of cardboard needed to make the
  container is to be a minimum.

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• Ex.4
• This container is to hold a volume of 1600cm3.
• The length is to be three times the breadth.
• The area of cardboard needed to make the
  container is to be a minimum.