Discuss the trade-offs a firm faces when setting the profit-maximizing two-part tariff in this setting. Under what conditions does an increase in the per-unit price increase total profit?

The individual inverse demand for customers in group one equals: P1 = 20 - q1. The individual inverse demand for customers in group 2 equals: P2 = 20 - 2q2. The marginal cost of production is constant and equal to $2/unit. Assume an equal number of customers in each group.