A firm can hire as much labor as it wants at \($5\) per hour. In return, each worker produces 10 units of output per hour. The firm can sell up to 2,500 units of output each day at \($2\) per unit, but it cannot sell any more than 2,500 units of output in a day. The firm has no other costs besides labor.

(a) How many hours of labor does the firm purchase and how much profit does it earn each day?

(b) The firm can choose to pay an efficiency wage. In particular, the firm can choose to pay \($6,\) \($7,\) \($8,\) \($9,\) or \($10\) per hour, and in exchange, each worker will produce 18, 23, 27, 28, or 29 units of output per hour, respectively. What hourly wage should the firm offer to maximize profits?