2. A firm wants to maximize its profit from producing two different products, A and B. The demand for product A is given by P = 50-3Q where QA and PA are quantity and price of product A, respectively. While the demand for product B is given by Pa = 70-50s where Qu and Ps are quantity and price of product B, respectively. Total cost for producing those two goods are given by TC=250-20+400-30% +QaQs + 100. Given the information, please answer the following question: a. Find the profit function for the optimization problem above! [5 points] b. Find the optimal numbers of product A and B that need to be produced by the firm and then calculate the firm's profit! [hints: use first order condition] [10 points] c. Check whether the profit from your calculation is maximum! [hints: use second order condition] [10 points]