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The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $944/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 $8 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?

Respuesta :

69 Passengers (20 plus additional 49) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $38,088.

current: 20 passengers at $944 each

let the number of additional passengers be x

cost per passenger = 944 - 8x

revenue (R) = (20+x)(944-8x)

= 18880 - 160x + 944x -8 x^2

dR/dx = -160 + 944 - 16x = 0 for a max of R

16x = 784

x = 49

There should be an additional 49 or a total of 69 passengers

The cost per passenger would be 944-8(49) or $552 per day

Maximum revenue for the yacht:

revenue (R) = (20+x)(944-8x)

revenue (R) = (20+49)(944-8(49))

revenue (R) = (69)(944-392)

revenue (R) = $38,088

Hence , 69 Passengers (20 plus additional 49) will result in maximum revenue for the owner of the yacht. Maximum Revenue will be $38,088.

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