Answer:
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
