Question

A park offers group tours for 100 to 300 people at a time. For every person over 100, the cost for each ticket is reduced by one cent off the normal s4 per person charge. Find the number of people in the group that yields the maximum total cost for the group and also find the number of people in the group that yields the minimum total cost for the group.

Answer 1

Let x be the number of people over 100. Then the cost is
c(x) = (100+x)(4.00 - 0.01x) for 1 <= x <= 200
The vertex (max) of this parabola is at (150,625)
c(100) = 400
c(300) = 600
400 is the minimum in the given domain.