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 - 4P_{1}
Q_{d2}=90 - 2P_{2 } where the subscripts 1 and 2 refer to product 1 and product 2, respectively. The firm now faces a total cost function: TC= Q+150where Q= Q_{1} + Q_{2}
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.