thanks in advance

Suppose we have a duopoly market, with two firms. Suppose first that firms 1 and 2 produce perfectly homogeneous products, in the sense that they sell their output at a price that depends only on the total amount produced in the market and not on who does the producing. Hence, the firms solve the following optimization problems: max *1 ($1, 12) = max(100 - 3r] - 312)r] - 1011 FI max #2($1, 12) = max(100 - 3r2 - 3x1)12 - 1012. (a) Find the equilibrium quantities of output for these firms, the equilib rium price, and the profits earned by each firm. To see how we might allow for heterogeneous products, let the firms solve the following problems where a > 0, b > 0: max #1 ($1, 12) = max(a - br1 + 9x2)31 - cr1 max *2(X1, 12) = max(a - bx2 + 931)12 - CT2. (b) Explain whether you expect g to be positive or negative, in terms of whether these goods are substitutes or complements. (c) Find the equilibrium quantities of z, and ry in this market. To do this, find the first-order condition for each firm, and solve the resulting pair of linear equations for r, and 12. (d) Is firm 1 in this market better off when g is positive or negative? Why