The manager of a firm wants to implement a two-part pricing for a product having two different types of consumers. The market has 10 consumers with a lower willingness to pay with a demand curve given by Q1 = 8 - P, and 10 consumers with a higher willingness to pay with a demand curve given by QB = 10 - P. The marginal cost (and the average cost) is constant at 2, and there are no fixed costs. Assume that he sets only one entry fee and one usage fee.

a. For two-part pricing problem above, write down the detailed profit function for the manager. Use the information given above and show clearly all the components of the function. Remember that he is solving for the profit- maximizing price. 

b. After his calculations, he finds that the profit -maximizing price is $3 per unit. Find the entry fee that he'll charge his customers.