Case scenario of wet-n-wild indoor water park

Question

Problem:

Wet-n-Wild Indoor Water Park offers family fun year-round in the Northstar state to locals and out-of-state visitors to the nearby Mall of America. The demand for day-passes to the water park for each market segment is independent of the other market segment. The marginal cost of providing service to each visitor is $5 per day. Suppose the daily demand curves for the two market segments are:

Locals - Q_L=3000-200P or P=15-0.005*Q_L

Out of towners - Q_O = 3000-100P or P=30-0.01*Q_O

Question 1: If Wet-n-Wild Indoor Water Park charges one price to all visitors, what is the profit maximizing price? How many day-passes will be sold per day?

Question 2: If Wet-n-Wild Indoor Water Park charges one price to locals, what is the profit maximizing price for locals? How many day-passes will be sold per day to locals?

Question 3: If Wet-n-Wild Indoor Water Park charges one price to out-of-towners, what is the profit maximizing price for out-of-town guests? How many day-passes will be sold per day to out-of-town guests?

Question 4: Compare the prices from uniform pricing to the prices from price discrimination.