Getthere airlines currently charges $200$ dollars per ticket and sells $40{,}000$ tickets a week. for every $10$ dollars they increase the ticket price, they sell $1000$ fewer tickets a week. how many dollars should they charge to maximize their total revenue?

Suppose GetThere Airlines increases their ticket price to $200+10n = 10 (20+n) $ dollars. Then the number of tickets they sell is $40,000-1000n = 1000 (40-n) $. Therefore, their total revenue is

$$10 (20+n) / cdot 1000 (40-n) = 10000 (20+n) (40-n) = 10000 (800+20n-n^2).$$

This is maximized when $n=-/left (/frac{20}{2/cdot (-1) }/right) = 10$. Therefore, they should charge $200+10/cdot 10 = / boxed{300}$ dollars per ticket.