Answer:
58 passengers
Step-by-step explanation:
Capacity of the cruise ship = 68 people
Minimum number for an excursion = 46 people
Maximum cost per person = $ 70
Let the additional passenger = y
y minimum =1
y maximum = 68- 46
= 22
y can be represented in the inequality below:
1 ≤ y ≤ 22
New ticket cost of excursion for every added passenger = (70-y)
Total passengers = (46+y)
Income (I) = (70-y) (46+y)
= 3220 + 70y -46y - y²
= 3220 +24y -y²------------------------------- (1)
To maximize the income function I (y) in equation (1), dI/dy =0 , and (1) becomes :
24-2y = 0
2y = 24
y =12
So the total number of passengers that maximizes income is :
= (46+y)
= (46+12
= 58 passengers
