In the faraway town of Saint James two firms, Bilge and Chem, compete in the soft-drink market (Coke and Pepsi aren't in this market yet). They sell identical products, and since their good is a liquid, they can easily choose to produce fractions of units. Since they are the only two firms in this market, the price of the good (in dollars), P, is determined by P = (30 - Q_B - Q_c), where Q_B is the quantity produced by Bilge and Q_c is the quantity produced by Chem (each measured in liters). At this time both firms are considering whether to invest in new bottling equipment that will lower their variable costs. (i) If firm j decides not to invest, its cost will be C_j =