A firm faces perfectly elastic demand for its output at a price of $6 per unit of output. The firm, however, faces an upward-sloped labor supply curve of
E = 20w - 120
where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces an upward-sloped marginal cost of labor curve of
MCE = 6 + 0.1E
Each hour of labor produces five units of output. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay? What are the firm's hourly profits?