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.

TableWardrobeTotal available per month Wood2 packs3 packs36 packs of wood Labour2 days1 days20 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? TableWardrobeTotal available per month Wood2 packs3 packs36 packs of wood Labour2 days1 days20 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.