What number of passengers will maximize revenue?

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Homework Help Overview

The discussion revolves around maximizing revenue for a travel package plan, specifically focusing on the relationship between the number of passengers and the associated revenue. The problem involves fare structures and constraints related to passenger capacity and minimum requirements.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the formulation of a revenue equation based on passenger numbers and fare structures. There are attempts to derive a maximum revenue condition through calculus, with questions raised about the derivation process of the revenue equation.

Discussion Status

Some participants have provided guidance on deriving the revenue equation and checking for maximum values. There is an acknowledgment of the constraints regarding passenger numbers, but no explicit consensus on the derivation process itself.

Contextual Notes

The problem includes constraints such as the maximum capacity of 120 passengers and a minimum requirement of 50 passengers for the flight to proceed. The fare structure is also a key element under discussion.

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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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[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.
 
thanks for your help. I got the right answer.
 
how was the equation gotten
pls expalin
 
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)
 

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