Input profit optimization problem. A firm sells a product at a unit price of £ 8, while the production function to produce this type of item is represented by the following CobbeDouglas function: q ¼  L1=8 K3=8  The unit prices of inputs are pL ¼ 4, pK ¼ 12. The profit function is therefore given as usual by: p ¼ pq  TC ¼ 8 $  L1=8 K3=8   4L  12K Find the optimal demand of inputs that maximizes the profit p.