Suppose a firm's total cost function is given by TC = 100 + 4Q + 0.02Q^2, where Q is the quantity of output produced. The firm faces a market price of $10 per unit.

a) Calculate the profit-maximizing level of output and the corresponding profit.

b) Suppose the government imposes a tax of $1 per unit sold on this market. Calculate the new profit-maximizing level of output, the amount of the tax revenue collected by the government, and the after-tax profit of the firm.