A carpenter builds and sells her own chairs and beds. To build a chair it takes 6m? of wood and 12m2 of fabric. To build a bed it takes 1Om? of wood and 9m? of fabric. The price of wood and fabric are 12 and 18 per m, respectively. The carpenter buys 84 m2 of wood and 108 m of fabric each month. The selling price of a chair is 300 and for a bed it is 310. What number of chairs and beds should the carpenter build each month to maximise her profit? Calculate any possible shadow prices. [10 marks]