Problema Solution
A small cruising ship that can hold up to 68 people provides three-day excursions to groups of 4646 or more. If the group contains 46 people, each person pays $70. The cost per person for all members of the party is reduced by $1 for each person in excess of 46. Find the size of the group that maximizes income for the owners of the ship.
Answer provided by our tutors
The function that represents the income is:
F(x) = 46*70 + (x - 46)*(70 - 1), where 'x' is the number of people and 46 < = x <= 68
F(x) = 69x + 46
Since the function F(x) = 45x + 1150 is increasing the size of the group that maximizes income is 68.