The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $408/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 100) for the cruise, then each fare is reduced by $4 for each additional passenger.Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht. What is the maximum revenue? What would be the fare/passenger in this case? (Round your answer to the nearest dollar.)

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Asked Oct 18, 2019
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The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $408/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 100) for the cruise, then each fare is reduced by $4 for each additional passenger.

Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht.

 

What is the maximum revenue?

 

What would be the fare/passenger in this case? (Round your answer to the nearest dollar.)

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Expert Answer

Step 1

Let x be the number of additional passengers.

For additional x passengers, the revenue becomes,

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Revenue - (408-x(4))x (20+ x) R(x)(408-4x)(20+ x)

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Step 2

Obtain the critical points to find th...

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R'(x)=0 (408-4x)(20 x)]0 dx (408-4x)(1)(20+ x)(-4)= 0 408-4x-80-4x = 0 328-8x 0 328 8.x x = 41

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