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This is a sample of full context cases. You may go back to the main Consulting Math 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 newly started airline with only one Boeing 737 in its fleet. Currently the B-737 contains 200 economy seats. The airline is considering to install business and first class seats into the plane.
management consulting prep pst full context cases 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 150 economy seats only and 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 seat type 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, 20 business class seats. With the demand stated in the last question (200, 10, 4), what is the maximum revenue the airline can generate in one flight? Assuming that the airline will use all possible strategies to generate the most revenue in that one flight.

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1.1: 76%
Current Revenue: 200 x $100 = $20000
Future Revenue: (150 x $100) + ($200* a) = $20000.
<=> 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 = 76% (25 out of 33)

1.2: 177 seats
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
Demand for a First Class seat is 4, which leaves 6 vacant First Class seats. These seats can be split back into 12 Economy class seats to generate more revenue. Likewise, there will be 10 vacant Business class seats. However, these will be more difficult to split since 1 Business class seat = 1.5 Economy class seat. Nevertheless, with the stated assumption, there should be an extra 15 Economy class seats ready to be used. The original number of Economy class seats would be 200 – (10 x 2) – (20 x 1.5) =150 seats. Afterwards, with a total of 27 extra Economy class seats, there will be 177 Economy class seats, along with 4 First Class seats and 10 Business class seats.
Revenue = (4 x 500) + (10 x 200) + (177 x 100) = $21,700.

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  • Blake Shapskinsky

    In your first answer (1.1), you conclude with “Percentage = 50% (25 out of 50).” Should it not read “Percentage = 76% (25 out of 33)?”
    Thanks for this website, it is awesome.

    • MConsultingPrep

      Thanks for your shrewd observance Blake! Hope you find our Consulting Math materials useful to your study!

  • stuart head

    The answer to question 1.3 is a bit unlikely, I have to say. The question asks the maximum revenue for one flight, so I doubt this should include the possibility to rebuild the plane to change seats, as this will obviously not be done for each flight depending on the number of specific tickets bought. Alternatively, you can say that the unsold first and business class tickets were sold as economy tickets (with a free upgrade) so revenue = (4*500) + (10*200) + (166*100) = 20600.
    Moreover, the question will just basically be the same as 1.2 if you do it in the manner that is currently applied.

    • Anh Thai

      I agree with you here. Since it stated the plane was already built with 20 business class and 10 first class, so the remaining from the demand should be 16 seats in total. It’s unlikely for them to sell 1 first class seat to 2 people and 1 business class seat for 1.5 people. 1 customer can only occupy 1 seat. It would be illegal to have 2 people in 1 seat for safety purpose. So it would not make any sense to have 177 economy class seats, hence the airline is forced to sell the remaining 16 tickets for $100 under economy price. Total for all economy seats would be 166*100. The answers for most problems on this site seem to be unclear to me or no solution at all. It makes me question their service and training program.

      • Matt

        I would even argue that you could sell the leftover 1st class seats at business class price (free upgrade) and then the remaining business class seats as economy (also free upgrade). That would provide a total revenue of $22.2k

        Also on 1.2, wouldn’t you have 177 economy, 10 business and 4 1st class seats? Making the total # of seats in the plane 191. The 4 1st class seats will take up 8 economy seats, the 10 business seats will take up 15 economy seats. 200-8-15 = 177 remaining economy seats.

  • Ondrej Skala

    I believe 1.1 is 75% (50/1.5=33.33333) and 25/33.333333 is 75%

    • Cameron Duncan

      This is a bit late to the party, but if we think of it logically we would not add 33.3 business class seats. We would only be able to fit 33 seats into the plane…. unless someone wants to buy a ticket for a 3rd of a seat ; ). Always important to remind oneself of the context of the business problem and not get sucked into the numbers.