Question

A small cruising ship that can hold up to 50 people provides three-day excursions to groups of 30 or more. If the group contains 30 people, each person pays $66. The cost per person for all members of the party is reduced by $1 for each person in excess of 30. Find the size of the group that maximizes income for the owners of the ship.

Answer 1

To find the size of the group that maximizes income for the owners of the ship, we need to determine the number of people that will minimize the cost per person while accommodating the maximum number of passengers.

Step-by-step explanation:

To find the size of the group that maximizes income for the owners of the ship, we need to determine the number of people that will minimize the cost per person while still accommodating the maximum number of passengers.

We know that for a group of 30 people, each person pays $66. The cost per person is then reduced by $1 for each additional person. Let's set up an equation to find the optimal group size:

Cost per person = $66 - ($1 x Number of people over 30)

Let's solve this equation by setting the cost per person equal to zero:

$66 - ($1 x Number of people over 30) = 0

Now we can solve for the number of people over 30:

Number of people over 30 = $66 / $1 = 66

So the size of the group that maximizes income for the owners of the ship is 30 + 66 = 96.