A small cruising ship that can hold up to 70 people provides three-day excursions to groups of 44 or more. If the group contains 44 people, each person pays $72. The cost per person for all members of the party is reduced by $1 for each person in excess of 44. Find the size of the group that maximizes income for the owners of the ship.

Let, extra number of people are x.

it is given that cost per person for all members of the party is reduced by $1 for each person in excess of 44.

So, total cost C :

Now, dC/dx = 0

Total person on cruise 44 + 14 = 58 i.e less than the capacity.

Therefore, maximum income for the owner is for group of size 58.

Hence, this is the required solution.

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)