3. The East Company and the West Company are the only two firms that produce and sell a specialized type of machinery. The market demand curve for the machinery is as follows: P = 25 -0.0005 Q In this equation, P is the price of the machinery in dollars and Q is the total amount demanded. The total cost function for the East Company is as follows: TCEast = 4 Q+ 0.001 Q?East In this equation, TCEast is total cost in dollars and QEast is the output. The total cost function for the West Company is as follows: TCWest = 10 Q+ 0.001 Q?west In this equation, TCwest is total cost in dollars and Qwest is the output. a. If these two firms are successful in forming a cartel, determine (i) the profit-maximizing outputs for the East and West Companies, (ii) the profit-maximizing prices for the East and West companies, and (ii) the total profits for the East and West Companies.