Question Description
On a popular route, an airline offers two classes of service: business class (B) and economyclass (E). The respective demands are given by:
𝑃B =540− .5𝑄B and 𝑃E =380− .25𝑄E
Because of ticketing restrictions, business travelers cannot take advantage of economy’s lowfares. The airline operates two flights daily. Each flight has a capacity of 200 passengers. Thecost 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 airlineshould sell. Your spreadsheet should include revenue and marginal revenue for each type ofticket, total revenue, marginal cost, total cost, and profit. Your only choice variables shouldbe the number of business class tickets and the number of economy class tickets. All othervalues (aside from the seats per plane and total cost per trip) should be computed based onyour choice variable.
- By hand, solve for the fares the airline charge should charge to maximize revenue. Howmany passengers will buy tickets of each type? Check your answer with your spreadsheetsolver. (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 togive 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 theplane. Find the optimal single fare using the spreadsheet solver. (Hint: you can think ofthe ‘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 withthe airport they face the cost curve 𝐶 = 20000 + 5000𝐹2 where F is the number of flights perday. Assume the airline uses the optimal fares from part a.
c. By hand, solve for the profit maximizing number of flights. Check your answer with yoursolver. Also report the total revenue and profit.
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