Question

QUESTION 12 A travel agency is planning a trip to England for 100 members of a college faculty. The plane fare will be $600 per faculty member ifall 100 members attend the trip. With each cancellation, however, the fare will increase by $20 per faculty member. What is the number of passengers that will generate the maximum revenue for the agency? a. 35 b. 40 0.60 d.65 QUESTION 13 12. A travel agency is planning a trip to England for 100 members of a college faculty. The plane fare will be $600 per faculty member if all 100 members attend the trip. With each cancellation, however, the fare will increase by $20 per faculty member. If the cost to the agency is $20,000 plus $40 for each passenger, what is the fare that will maximize profit? a $1,320 b. $1,300 c. $600 d.$64

Answer 1

12)

The fare and the number of cancellations are related as

Fare(F) = $600 + $20*Cancellations(C)

-> F = 600 + 20C

Now, Revenue = F*(100 - C)

= (600 + 20C)*(100 - C)

=

60000 + 14000 – 2002

To maximize revenue, we need to differentiate revenue w.r.t C and equate it to zero

-> 1400 - 40C = 0

-> C = 35

Thus, the required number of passengers = 100 - C

= 65

13)

TC = 20000 + 40(100 - C)

F = 600 + 20C

Profit = F*(100 - C) - TC

= 36,000 + 1440C - 20C^{2}

To maximize profit, we need to differentiate Profit w.r.t C and equate it to zero

-> 1440 - 40C = 0

-> C = 36

Thus,the fare that will maximize profit = 600 + 20*36

= $1,320