5. There are n firms in a competitive industry. The market demand function is given by p = 10 - Q. A firm's cost function is c (q) = ,q2. The government provides a proportional subsidy rate s > 0 for firms to help them get through the difficult time of a pandemic. That is, the firm earns (1 + s) p for each unit of goods sold. Show that the the total surplus strictly increases with s