Question: A firm manufactures two compounds A and B using two raw materials R and Q, in addition to labour and a mixing additive. Input requirements per tonne are:
For A: 1 container of R, 3 sacks of Q, 4 hours labour and 2 tins of mixing additive
For B: 2 containers of R, 5 sacks of Q and 3 hours labour, but no mixing additive
Both A and B add £200 per tonne to the firm's profits and it has at its disposal 60 containers of R, 150 sacks of Q, 120 hours of labour and 50 tins of mixing additive.
What combination of A and B should it produce to maximize profits, assuming that fractions of a tonne can be manufactured? What will these profits be? What surplus amounts of the inputs will there be?