(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $600 per person per day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $4 for each additional passenger.

(a) 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.

passengers

(b) What is the maximum revenue?

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

3. The attempt at a solution

No idea, could you just help me out on how to even start this problem? Cause i am clueless...

i did it this way, but did not really use optimization i think.

N= # of passengers

600-4N= fare

Revenue= 600N-4N^{2}

max at -> derivative of 0=600N-4N^{2}

0=600-8N

N=600/8

N=75 passengers

600-4(75)= 300$ a passenger

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# Optimization using differentiation

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