arted: Mar 14 at 10:50pm uiz Instructions DQuestion 12 2 pts fly Airlines has a

Question

arted: Mar 14 at 10:50pm uiz Instructions DQuestion 12 2 pts fly Airlines has a daily flight from Sacramento to Las Vegas with a capacity of 100 passengers. Offwef On average, 18 ticket holders cancel their reservations at the last minute, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a standard deviation of 1.9. Profit per passenger is $126. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $54. What is the optimal probability of having one or more empty seats on the plane? Next Previous Not saved Submit Quiz

Explanation / Answer

Given: Physical Flight capacity = 100 passengers

Compensation cost per pessenger in case of emergency, let denote it by C= $54

Profit per passenger or opportunity cost per passenger, let denote it by P= $126

let the total no. of last minute cancellation be = X

let the total no. of overbooked ticket be = Y

Now,

Optimality equation,

Total cost of overbooking should be balanced with revenue loss dute empty seats.

mathematically: C*probabilty(overbooking) = P*probablity(Having empty Seats)

can be rewritten as; C*pr(Y>X) = P*pr(Y<X)   

(According to probability Rule; pr(Y>X) + pr(Y<X) = 1 or, pr(Y>X)= 1- pr(Y<X))

Putting all the Values in above equation: C*pr(Y>X) = P*pr(Y<X)

54*{1-pr(Y<X)} = 126*pr(Y<X)

after solving above equation we get, pr(Y<X) = 0.30

i.e Optimal Probabilty of having one or more seats empty = 0.30

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.