6. ( 20 pts) Suppose a competitive firm produces two products. Let Qi represents the output level of the i-th product and let the prices of the products are denoted by P1 and P2. Since the firm is a competitive firm, it takes the prices as given. Accordingly, the firm's revenue function will be TR=P1Q1+P2Q2 The firm's cost function is assumed to be C=2Q12+Q1Q2+2Q22. 1) Write down the firm's profit function. 2) The firm wants to maximize the profit by choosing the levels of Q1 and Q2. Please use Cramer's rule to find the optimal solution for this purpose. 3) Please use the Hessian matrix to check the solution does maximize. 4) Given the demand function Q1 solved from part 2), find the price elasticity of demand for product 1 and interpret the answer, if p1=2 and p2=4