Two manufacturers, denoted 1 and 2, are competing for 100 identical customers. Each manufacturer chooses both the price and quality of its product, where each variable can take any nonnegative real number. Let p; and x;denote, respectively, the price and quality of manufacturer i's product. The cost to manufacturer i of producing for one customer is 10 + 5x; Note in this expression that the cost is higher when the quality is higher. If manufacturer i sells to q;customers, then its total cost is 9/10 + 5x). Each customer buys from the manufacturer who offers the greatest value, where the value of buying from manufacturer iis 1,000 + x;- pi, higher quality and lower price mean more value. A manufacturer's payoff is its profit, which equals q/P;-10-5x). If one manufacturer offers higher value, then all 100 customers buy from it. If both manufacturers offer the same value, then 50 customers buy from manufacturer 1 and the other 50 from manufacturer 2. Find all symmetric Nash equilibria