An airline is deciding how many tickets to sell for a flight to Indianapolis. The flight has 142 seats available. To simplify things, assume that first class is completely booked and all seats are in economy. Based on past flights, it is believed that 92 percent of those with a reservation will actually show up. Also assume that these are all individual passengers and not groups of passengers, so each decision to show up or not show up is independent. Each seat sells for $435. If a seat is sold but unused, the airline still gets to keep the money from the sale, so there is no lost revenue. However, if the airline oversells the cabin and more than 142 customers show upfor the flight, the airline will need to make other arrangements for these travelers. The cost of placing these extra travelers in other flights and vouchers for getting them to switch flights is $1600 per extra passenger who doesn't fit on the plane. How many seats should the airline sell for this particular flight to maximize the profit (narrowly defined here as ticket sales revenue minus the cost to reallocate extra passengers).

On an excel, what would the formula look like when you calculate the number of people showing up and probability along with profit up to 280 seats.