Asmall cruising ship that can hold up to 62 people provides three-day excursions to groups of 42 or more. if the group contains 42 people, each person pays $60. the cost per person for all members of the party is reduced by $1 for each person in excess of 42. find the size of the group that maximizes income for the owners of the shi

51

Step-by-step explanation:

You can figure this out by making a simple function to represent the problem

This is the function you would get:

f(x) = (x + 42) (60 - x)

The x is the number of people above 42. so it the group contains just 42 persons, x is going to be 0= each person is going to pay 60 so the total is going to be 2520

T he domain for x would be all integers from 0 to 18. Now all you have to do is determine which value of x will cause the value of f(x) to be the highest.

f(x)=(x + 42) (60 - x)=60x-x^2+42*60-42x=-x^2+18x+2520

to find the highest value, you could find the maximum by derivating and equal to 0.

f'(x)=-2x+18=0--->x=9

So the size of the group that maximizes income for the owner is 51 persons

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.