Final answer:
The cruise ship needs to book at least 410 passengers to be profitable.
Step-by-step explanation:
To determine the number of passengers that need to be booked for the cruise ship to be profitable, we need to find the difference between the capacity of the ship and the minimum number of passengers required. The capacity of the ship is 2462 passengers and the minimum number of passengers for profitability is 2052. Subtracting these two numbers, we get:
2462 - 2052 = 410
So, the cruise ship needs to book at least 410 passengers to be profitable.