The  firm  is  considering  manufacturing  a  second  product  in  its  factory
alongside the first. The demand functions for the two products are:

Q_d1=180 - 4P₁

Q_d2=90 -  2P₂

 
where the subscripts 1 and 2 refer to product 1 and product 2, respectively.
The firm now faces a total cost function:
TC=   Q+150
where  Q= Q₁ + Q₂

a) Dtermine the new total profit function for the firm as a function of Q1  and Q2.

b)  Using your new profit function measured in part (b)(i) find the level of output  for every product at the profit maximising point and display your outcome is a maximum.