What number of passengers will maximize revenue?

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To maximize revenue for New Horizons Travel, the fare structure includes a base price of $400 per passenger and an additional $8 for each unsold seat. The total revenue equation is derived as MONEY = kn + (120 - n)k'n, where k is the fare and k' is the cost per empty seat. By taking the derivative of this equation with respect to the number of passengers (n) and setting it to zero, the optimal number of passengers is determined to be 85. This figure is within the operational constraints, as the flight requires a minimum of 50 passengers to avoid cancellation. Understanding the revenue model is crucial for maximizing profitability in this scenario.
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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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MONEY=kn+(120-n)k'n,
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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