Come on in, the modeling expert of overbooking.

Your question looks like an airline's revenue management problem, but the airline's revenue management still needs to consider the sales quantity decision of multi-level fares.

According to the assumptions in the title, it is obvious that the problem has been simplified. And the answers to questions (1) and (2) should be the same.

The biggest profit of this flight is:1500 *150 = 225,000 yuan (load factor 100%, noshow).

No matter how to optimize and sell, it is impossible to get a higher income than this, so the optimized income should be less than and closest to this maximum income.

Assuming that the no-show rate of each passenger is 4%, the loss is the smallest and the gain is the largest when selling X air tickets, then the number of no-shows at this time is Y.

The amount that each noshow passenger needs to pay is1500+1500 * 20% =1800 (assuming the settlement is full price).

Then the flight income is: 1500x- 1800y.

And Y=X*4%, substituted into the above formula, the flight income is: 1428X.

Let 1428X be infinitely close and less than 225000, and x is an integer, then it is not difficult to get X= 157.

So the answer is that when you sell 157 tickets (when you sell more than 7 tickets), the loss is the smallest and the gain is the largest.

In 2007, the Civil Aviation Administration of China issued a document prohibiting overselling to airlines, and will be fined if it violates it. Don't think you can get away with it, because the data in eterm will be known as soon as you check it.