Data for a Poisson with mean 10 A BigJet flight from Philadelphia to Boston has 60 seats. The high fare is $400 and the low fare is $100. There is ample demand for the low fare class and they buy well in advance before high fare customers Demand for the high fare is Poisson with mean 10, 1 0.000 0.000 2 0.002 0.003 3 0.008 0.010 40.019 0.029 5 0.038 0.067 60.063 0.130 7 0.090 0.220 80.113 0.333 9 0.125 0.458 100.1250.583 11 0.114 0.697 12 0.0950.792 13 0.073 0.864 14 0.052 0.917 15 0.0350.951 00.000 0.000 10.0 9.0 8.0 7.0 6.0 5.0 4.1 3.2 2.5 1.8 1.3 0.8 0.5 0.3 0.2 0.1 To choose a protection level ... What is Co? What is Cu? What is the optimal protection level? With the optimal protection level ... How many high fare seats can then expect to sell? What is the probability of a full flight? What is the optimal booking limit?

Question

Ashtyn

Business

26 August, 13:45

Data for a Poisson with mean 10 A BigJet flight from Philadelphia to Boston has 60 seats. The high fare is $400 and the low fare is $100. There is ample demand for the low fare class and they buy well in advance before high fare customers Demand for the high fare is Poisson with mean 10, 1 0.000 0.000 2 0.002 0.003 3 0.008 0.010 40.019 0.029 5 0.038 0.067 60.063 0.130 7 0.090 0.220 80.113 0.333 9 0.125 0.458 100.1250.583 11 0.114 0.697 12 0.0950.792 13 0.073 0.864 14 0.052 0.917 15 0.0350.951 00.000 0.000 10.0 9.0 8.0 7.0 6.0 5.0 4.1 3.2 2.5 1.8 1.3 0.8 0.5 0.3 0.2 0.1 To choose a protection level ... What is Co? What is Cu? What is the optimal protection level? With the optimal protection level ... How many high fare seats can then expect to sell? What is the probability of a full flight? What is the optimal booking limit?

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Answers (1)

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Madilyn Hanna · Answer 1

Consider the following calculations

Explanation:

Co = low fare = $ 100

Cu = high fare - low fare = 400 - 100 = $ 300

Critical ratio = Cu / (Cu+Co) = 300 / (300+100) = 0.75

In the table, look for F (q) > = 0.75, that value is 0.792 and corresponding value of q = 12. Therefore,

Optimal protection level = 12

Refer the table for q=12, Expected shortage, L (q) = 0.5

Expected high fare seats to be sold = Mean demand - Expected shortage = 10-0.5 = 9.5

Probability of a full flight = 0.792