A barber charges $12 per haircut and works Saturday through Thursday. He can perform up to 20 haircuts a day. He currently performs an average of 12 haircuts per day during the weekdays (Monday through Thursday). On Saturdays and Sundays, he does 20 haircuts per day and turns 10 potential customers away each day. These customers all go to the competition. The barber is considering raising his prices on weekends. He estimates that for every $1 he raises his price, he will lose an additional 10% of his customer base (including his turnaways). He estimates that 20% of his remaining weekend customers would move to a weekday in order to save $1, 40% would move to a weekday in order to save $2, and 60% would move to a weekday in order to save $3. Assuming he needs to price in increments of $1, should he charge a differential weekend price? If so, what should the weekend price be? (Assume he continues to charge $12 on weekdays.) How much revenue (if any) would he gain from his policy?

Please provide the answer and any hints or work to go along so I can use to study for upcoming tests.