We are reviewing our Uber surge pricing strategy and we are thinking about enacting a bar-district surge price. We have studied demand characteristics of rides in major cities with well-known bar districts. Furthermore, our data analytics team has estimated the inverse demand P₁(Q₁) for rides to bar districts before 2am and the inverse demand P₂(Q₂) for rides from bar districts after 2am, as follows:

Group 1: rides to bar districts before 2am: P₁(Q₁) = 5 - 0.01Q₁

Group 2: rides from bar district after 2am: P₂(Q₂) = 10 - 0.01Q₂

First, note that these price functions are in per mile terms. Also, keep in mind that our marginal costs per mile driven is $1.

Please review optimal prices to charge to each group (using 3^rd degree price customization) and let me know what the resulting profits would be.