In the original theme park example (capacity = 1000) , suppose the prices cause diversion. Some weekend buyers (Saturday or Sunday) will switch between weekend days, but they never switch to a weekday. Some weekday buyers will switch to any other day (weekdays or weekends) if the price is better. Weekday buyers switch at a rate of 8 people per $1 price difference. Weekend buyers switch at a rate of 10 people per every $1 price difference (but again, switching only occurs between Saturday and Sunday or vice?versa). (a) What are the optimal daily prices? (b) What is the optimal revenue? (c) What is the daily attendance?

***The Theme Park Problem***

Another example related to entertainment is the Theme Park example (again, from Robert Phillips book

Pricing and Revenue Optimization, Stanford Press, 2005). In this example, business repeats every day just like a theme parkand each market segment corresponds to a particular day. Both the number ofpeople and their willingness to pay (price sensitivity) depend on the day of the week. This type ofsegmentation seems plausible for theme parks and other entertainment businesses that offer arepeatable experience each day of the week (e.g., ski areas, boat tours, etc.). People often self?select intoa particular day to find a price that matches their budget.

Capacity at the park is 1000 customers per day. The linear response functions on each day have anintercept (D) and slope (m) as given in the table below.

Day of Wee/ Intercept (Di)/Slope (mi)

Sunday/3100/?62

Monday/1500/?50

Tuesday/1400/?40

Wednesday/1510/?42

Thursday/2000/?52.6

Friday/2500/?55.6

Saturday/3300/?60

	Prices		Day	M	Di		Responses/Sales
p1	25.48754066		Sun	3100	-62		1000
p2	25.48754068		Mon	1500	-50		225.6229658
p3	25.48754069		Tue	1400	-40		380.4983726
p4	25.48754069		Wed	1510	-42		439.5232911
p5	25.48754068		Thu	2000	-52.6		659.35536
p6	25.48754071		Fri	2500	-55.6		1000
p7	25.48754073		Sat	3300	-60		1000
	Total Contribution
	119918.8787