Profit maximization
A beverage company produces two types of carbonated drinks, Drink L and Drink K, for which the average costs of production are constant at $5 and $6 per litre, respectively. The quantities q_L, q_K (in litres) of Drink L and Drink K that can be sold each week are given by the joint-demand functions
q_L=400\left(p_K-p_L\right)
q_K=400\left(9+p_L-2p_K\right)
Where q_A and q_B are the selling prices (in dollars per litre) of L and K, respectively. Determine the selling prices that will maximize the company’s profit, P.
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