A travel agency is chartering a flight for a minimum of 200 people. If exactly 2

Question

A travel agency is chartering a flight for a minimum of 200 people. If exactly 200 people sign up for the flight, the fare is set at $300/person. For each additional person who signs up, beyond the 200th, each passenger's fare is reduced by $1. Determine how many passengers will result in a maximum revenue for the agency. What is the maximum revenue? What would be the fare per passenger in this case?
Hint: start by explaning why the revenue function R is given by R(x)=(200+x)(300-x), where x >or equal to 0 is the number of passengers over 200.

Explanation / Answer

R(x)=(200+x)(300-x) when x persons increases fare of each person decreases by one.so total fare decreaced=x for maximum revenue dR(x)=0 (300-x)-200-x= x=50 persons maximum revenue=250*250=6250000dollars fare per passenger =250dollars

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