What number of passengers will maximize revenue?

  • Thread starter punjabi_monster
  • Start date
After deriving the equation with respect to n and setting it equal to zero, the value of n that will maximize revenue is 85, which is within the given constraints. The equation was derived by considering the cost for each seat and the number of passengers needed to maximize the revenue.
  • #1
punjabi_monster
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New Horizons Travel adversities a package plan for a vacation. The fare for the flight is $400/person plus $8.00/person for each unsold seat on the plane. THe plane holds 120 passengers and the flight will be canceled if there are fewer than 50 passengers. What number of passengers will maximize revenue?

i understand this is a revenue quesitosn but how do u start it off?

thanks.
 
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  • #2
[tex]MONEY=kn+(120-n)k'n[/tex],
where k=400, k'=8.

Derive with respect to n and find out for what value of n will the first derivation be zero. This must be a maximum for obviouse reasons. The answer you should get is 85, which is (thankfully) inside your constraints.
 
  • #3
thanks for your help. I got the right answer.
 
  • #4
how was the equation gotten
pls expalin
 
  • #5
how was the equation gotten

Every person needs to pay 400 dollars for their seat (kn) plus every person need s to pay 8 dolars for each empty seat ((120-n)k'n)
 

What is the significance of finding the maximum revenue for the number of passengers?

Finding the maximum revenue for the number of passengers is important because it helps determine the most profitable capacity for the transportation service. It can also provide insights on how to optimize pricing strategies and manage resources efficiently.

What factors affect the number of passengers that will maximize revenue?

The number of passengers that will maximize revenue is influenced by various factors such as the cost of the transportation service, demand for the service, competition in the market, and any external factors that may affect travel patterns.

How can data analysis help determine the number of passengers that will maximize revenue?

Data analysis can help determine the number of passengers that will maximize revenue by providing insights on passenger demand, pricing trends, and competitor strategies. This data can be used to create revenue optimization models and make data-driven decisions.

Is there a specific mathematical formula to calculate the number of passengers that will maximize revenue?

There is no one-size-fits-all formula to calculate the number of passengers that will maximize revenue. It varies depending on the specific transportation service, market conditions, and other factors. However, revenue optimization models can be created using mathematical and statistical techniques to determine the optimal number of passengers.

How can the transportation service continuously maximize revenue for the number of passengers?

The transportation service can continuously maximize revenue for the number of passengers by regularly analyzing data, adapting to changing market conditions, and implementing effective pricing and marketing strategies. It is also important to monitor and adjust the number of available seats based on demand and competition in the market.

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