Airline $1$ can charge $$100,$ $$200$ or $$300$ per seat. Airline $2$ can charge $$100$

or $$500.$ There are $40$ customers who will split according to the following rule: If one

airline is charging $$400$ more than the other $35$ go to the cheaper airline. If one

airline is charging $$300$ more then $30$ go to the cheaper airline. Otherwise the

customers split. Write down the payoff matrix and find all relations of weak

dominance.