Question

An airline finds that if it prices a cross-country ticket at $200, it will sell 300 tickets per day. It estimates that each $20

Answer 1

We can write that as a function:

$f(n)=(200 -20n) * (300 + 50n)\\f(n)=60000+10000n-6000n-1000n^2\\f(n)=-1000n^2+4000n+60000$

where $n$ is the number of price reductions. We can see that it is a quadratic function which has the biggest value at P = (p, q). It means that p is the number of reductions which results in the biggest profit.

$p=\frac{-b}{2a}=\frac{-4000}{-2000}=2$

It means that it's the best to make 2 price reductions for the company. The tickets should be sold for $200 - 2 * $20 = $160. It results in 2 * 50 more tickets sold which is 300 + 100 = 400.

Answer:

Ticket price: $160

Number of tickets: 400