Question

A travel agency offers group tours at a rate of $60/person for the first 30 participants. For longer groups-up to 90-each person receives a$0.50 discount for every participant in excess of 30. For example, if 31 participate, the cost/person is $59.50. Determine the size of the group that will produce the maximum amount of money for the agency.

Answer 1

revenue for x>=30

r = x(60-0.50(x-30))
= .5x(150-x)

max r at x=75