It costs a bus company 225$ to run a bus on a ski trip, plus 30$ per passenger. The bus has a seating capacity of 22 passengers. The company charges 60$ per fare if the bus is full. For each empty seat, the company has to increase the ticket price by 60$. Explain how to determine maximum profit.

Answer 1

wait. you say that if there are 22 passengers, each ticket costs $60
but if there is one empty seat, each ticket costs $120?
and if there are 2 empty seats, each ticket costs $180?
I don't think so!
But assuming that's so, let's go on, and you can fix it as needed.
Total cost for x riders: 225+30x
total revenue: 60(23-x)*x
profit: 60x(23-x)-(30x+225) = -60x^2 + 1350x - 225
the maximum profit is at the vertex, which I'm sure you can find...