The Retired Carpenter
An Investigation
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.
Table
Wardrobe
Total available
per month
Wood
2 packs
3 packs
Labour
2 days
1 days
36 packs of
wood
20 days
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?
Table
Wardrobe
Total available
per month
Wood
2 packs
3 packs
36 packs of wood
Labour
2 days
1 days
20 days


Solution
Let x = number of tables
Let y = number of wardrobes
Then x  0, y  0, 2x+3y  36, and 2x+y  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.