## Full-context cases

This is a sample of *word problems within full-context business case.* You might want to go back to the Consulting Math overview article for more in-depth information on improving your quantitative capabilities for the McKinsey PST and Case Interviews!

##### Case 1: Airplane sitting options

The client is a new airline with only one Boeing 737 in its fleet. Currently, the B-737 contains 200 Economy seats. The airline is considering installing business and First Class seats into the plane.

The space required per seat is how much space each type of seat requires measured by the number of Economy seats.**1.1:** Assume that Economy seats are always fully occupied. If the airline wants to have only 150 Economy seats and install business seats to fill up the rest of the plane, what is the minimum percentage of Business seats occupation needed to ensure that the airline has at least as much revenue as before?**1.2:** We know that the demand per flight for each type of seat is always 200, 10, 4, respectively (Economy, Business, First). What is the best seating allocation for the airline? Assuming the goal is to maximize its revenue.**1.3:** Assuming the client has already built the plane with 10 First Class seats and 20 Business Class seats, and that the airline will use all possible strategies to generate the most revenue in one flight. With the same seat demand stated in the last question (200, 10, 4), what is the maximum revenue the airline can generate in one flight?

### Answers

**1.1:** 76%

Current Revenue: 200 x $100 = $20000

Future Revenue: (150 x $100) + ($200* a) = $20000.

Thus, a = 25, which means at least 25 Business Class seats are needed to be occupied in order to ensure that the airline has at least as much revenue as before. Percentage: 25/33 = 76%

**1.2:** Since First Class seats obviously bring in much more revenue, the airline should put 4 First Class seats on every flight. Business Class seats also bring in more revenue so the airline should take full advantage of this and put 10 Business Class seats on every flight as well. The remaining seats will be Economy Class seats.

Revenue: (4 x 500) + (10 x 200) + (177 x 100) = $21,700. Note that 1 First Class seat = 2 Economy Class seats and 1 Business Class seat = 1.5 Economy class seats, so the remaining number of Economy Class seats are: 200 – (4 x 2) – (10 x 1.5) = 177 seats

**1.3:** $21,700

The demand for First Class seats is 4, which leaves 6 vacant First Class seats. These seats can be sold as 6 Economy Class seats to generate more revenue. Likewise, there will be 10 vacant Business Class seats. These can be sold as 10 Economy Class seat. The original number of Economy Class seats would be 200 – (10 x 2) – (20 x 1.5) =150 seats. Afterward, with a total of 16 extra Economy Class seats, there will be 166 Economy class seats, along with 4 First Class seats and 10 Business Class seats.

Revenue: (4 x 500) + (10 x 200) + (166 x 100) = $20,600.