A broking firm is a monopolistic producer of two transactions. The prices are related to quantities Q(1) and Q(2) according to the demand equations
P(1)=50-Q(1)
P(2)=95-3Q(2)
If the total cost function is
TC=Q(1)^2 + 3Q(1)Q(2)+ Q(2)^2
find values of Q(1) and Q(2) which maximize profit and deduce the corresponding equilibrium prices.