On a popular route, an airline offers two classes of service: business class (B) and economy class (E). The respective demands are given by:
B =540− .5Band E =380− .25E
Because of ticketing restrictions, business travelers cannot take advantage of economy’s low fares. The airline operates two flights daily. Each flight has a capacity of 200 passengers. The cost to the airline per flight is $20,000. The airline seeks to maximize total revenue.
Create a spreadsheet that can solve for the optimal number of each type of ticket the airline should sell. Your spreadsheet should include revenue and marginal revenue for each type of ticket, total revenue, marginal cost, total cost, and profit. Your only choice variables should be the number of business class tickets and the number of economy class tickets. All other values (aside from the seats per plane and total cost per trip) should be computed based on your choice variable.
- By hand, solve for the fares the airline charge should charge to maximize revenue. How many passengers will buy tickets of each type? Check your answer with your spreadsheet solver. (Hint: remember that the optimal occurs where marginal cost = marginal benefit, MC=MB, and in this case the cost of selling one more economy class ticket is having to give up a business class ticket, and vice versa). Also report the total revenue and profit.
- Suppose the airline is considering promoting a single “value fare” to all passengers on the plane. Find the optimal single fare using the spreadsheet solver. (Hint: you can think of the ‘single fare’ as an additional constraint.) Also report the total revenue and profit.
Now suppose the airline can vary the number of daily flights, but due to their contract with the airport they face the cost curve = 20000 + 50002 where F is the number of flights per day. Assume the airline uses the optimal fares from part a.
- By hand, solve for the profit maximizing number of flights. Check your answer with your solver. Also report the total revenue and profit.