The Retired Carpenter

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The Retired Carpenter

• An Investigation

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• The Retired Carpenter
• A retired carpenter decides to set up a small
  business for himself. Working from his garage,
  he decides to make tables and wardrobes which he
  then sells to the local furniture shop.
• He buys wood in packets from the Timber Merchant.
  In a monthly period he decides to devote a total
  of 20 days to his business and because of storage
  problems in his garage he is limited to buying a
  maximum of 36 packs of wood per month from the
  Timber Merchant. A table requires 2 packs of
  wood and 2 days labour. A wardrobe requires 3
  packs of wood and 1 days labour.
• These facts are set out in the table in the next
  slide.

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• On selling the finished product to the Furniture
  shop he is guaranteed to make a profit of 40 on
  each Table and 48 on each Wardrobe.
• How many of each should the carpenter make per
  month so that his monthly profit will be a
  maximum?

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• Solution
• Let x number of tables
• Let y number of wardrobes
• Then x 0, y 0, 2x3y 36, and 2xy
  20
• This is the old linear programming type of
  question and the expected method of solution
  would be to draw the feasible region and then
  apply the profit function
• P 40x 48y to each of the corner points
  (10,0), (0,0) (0,12) and (6,8) of the feasible
  region ending up with the solution 6 tables and 8
  wardrobes produce a profit of 626 per month for
  the carpenter.
• Pupils will probably try a trial and
  improvement method instead of the above and this
  will be fine.