In the beginning of every semester the study association W.S.G. Abacus of Applied Mathematics organizes a business trip. The organization has rent exactly one touring bus to transport the participants to the company, and the costs of €420 are evenly divided among all participants. On top of this, a small amount of €15 is charged per person for lunch and drinks during the day. Since the bus has only 24 available seats, only members from the study association are allowed to join the trip at first. Nevertheless, the organization decides to accept 5 interested students who aren’t part of the association because there is space left in the bus. By allowing these 5 extra students, the costs per person are reduced by €4,20.
a) Calculate how many students from the study association W.S.G. Abacus attend the trip, and what the participants have to pay per person.
Now assume the costs of the bus are no longer constant (yet still divided among all participants), but instead are given by the formula
Here C are the costs for the bus and x is the number of members from the association who participate. Assume that the 5 non-member students still join the trip.
b) Is it possible to achieve a minimum cost per person if you can decide how many members are allowed to participate? Justify your answer.