i need complete and clear answer please nuaicus, cunstaltits, and hüman consider
ID: 3354561 • Letter: I
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i need complete and clear answer please
nuaicus, cunstaltits, and hüman considerations of the issue. 6. [30 points] The airline's perspective. Overbooking is based on the phenomenon that not all passengers who buy tickets show up for their flight. Let: .n the number of seats on a flight. p- the price of a ticket. . the cost of bumping a passenger. X = the number of no-shows Assume X is a random variable uniformly distributed on {0,1,2,··· ·y = the number of tickets sold (decision variable). We will assume that p is fixed and the same for all seats, c is fixed and the same for any passenger, there is unlimited demand for this flight, and all tickets sold are non-refundable. (a) [5 points) Write down the airline's expected revenue for this flight as a function of y. (b) [6 points) Solve for the y' that maximizes the airline's expected revenue. (c) [2 points] For parameter values n = 200, p = $400, c = $1200, z = 20, calculate y. and the expected revenue at y? (d) [4 points] Suppose passengers never miss their flight, so z 0, Assuming the other parameter values remain the same as in part (c), what is y' and the expected revenue at y"? (e) [4 points] Suppose overbooking was not allowed, so the number of tickets sold is equal to the number of seats available. Assuming the parameter values remain the same as in part (c), how much would the airline charge for a ticket if it wanted to keep its expected revenue the same as part (c)?Explanation / Answer
Given,
n=number of seats in a flight
p=price of a ticket
c=cost of bumping a passenger
X=number of no shows
y=number of tickets sold
all tickets are non-refundable, it means to all the number of no shows(X) airlines will pay them zero
A.a) to calculate expected revenue
Cost to be incurred for bumping a passenger
Cost=c*no of passengers who show up above the capacity
Cost =c*(y-n-X)
Revenue=no of tickets sold*price of ticket
Revenue =y*p
Expected revenue=revenue-cost
Expected revenue =(y*p)-c*(y-n-X)
A.b) to maximize the revenue, the cost factor should be zero
i.e, c*(y-n-X)=0
y-n-X=0
y*=n+X or y-n=X
this implies that to maximize the profit, all the tickets booked(y) beyond the seats in the flight(n) should not showup(x). resulting in non-refundable cases and cost for airlines would be zero
A.c)given,
n=200
p=400
c=1200
x=20
calculate y* and expected revenue at y*
y*=n+x
y*=200+20=220
hence revenue is maximized at 220 bookings
expected revenue(y*)=(y*)(p)-c*(y*-n-X)
expected revenue(y*)=(220*400)-1200*(220-200-20)
expected revenue(y*)=88000
A.d) given,
n=200
p=400
c=1200
x=0
y*=n+x
y*=200+0=200
hence revenue is maximized at 200 bookings
expected revenue(y*)=(y*)(p)-c*(y*-n-X)
expected revenue(y*)=(200*400)-1200*(200-200-0)
expected revenue(y*)=80000
A.e)Given,
Expected revenue=88000
n=200
y=n=200
over booking is not allowed
hence x=c=0
Expected revenue =(y*p)-c*(y-n-X)
88000=200*p-0
p=88000/200
p=440
hence airlines should charge 440 per ticket to generate revenue of 88000
Given,
n=number of seats in a flight
p=price of a ticket
c=cost of bumping a passenger
X=number of no shows
y=number of tickets sold
all tickets are non-refundable, it means to all the number of no shows(X) airlines will pay them zero
A.a) to calculate expected revenue
Cost to be incurred for bumping a passenger
Cost=c*no of passengers who show up above the capacity
Cost =c*(y-n-X)
Revenue=no of tickets sold*price of ticket
Revenue =y*p
Expected revenue=revenue-cost
Expected revenue =(y*p)-c*(y-n-X)
A.b) to maximize the revenue, the cost factor should be zero
i.e, c*(y-n-X)=0
y-n-X=0
y*=n+X or y-n=X
this implies that to maximize the profit, all the tickets booked(y) beyond the seats in the flight(n) should not showup(x). resulting in non-refundable cases and cost for airlines would be zero
A.c)given,
n=200
p=400
c=1200
x=20
calculate y* and expected revenue at y*
y*=n+x
y*=200+20=220
hence revenue is maximized at 220 bookings
expected revenue(y*)=(y*)(p)-c*(y*-n-X)
expected revenue(y*)=(220*400)-1200*(220-200-20)
expected revenue(y*)=88000
A.d) given,
n=200
p=400
c=1200
x=0
y*=n+x
y*=200+0=200
hence revenue is maximized at 200 bookings
expected revenue(y*)=(y*)(p)-c*(y*-n-X)
expected revenue(y*)=(200*400)-1200*(200-200-0)
expected revenue(y*)=80000
A.e)Given,
Expected revenue=88000
n=200
y=n=200
over booking is not allowed
hence x=c=0
Expected revenue =(y*p)-c*(y-n-X)
88000=200*p-0
p=88000/200
p=440
hence airlines should charge 440 per ticket to generate revenue of 88000
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