An airline offers flights between three cities, $A,B$ and C according to the following network.

The fares for the ODFs are given in the table below. The airplanes used for flights A to B and B to C have $300$ and $350$ capacity, respectively.

$\backslash$table$[[$Number$,$ODF,Fare,Demand$],[1,$A to B full fare,$$150,150],[2,$A to B discount fare,$$50,170],[3,$B to C full fare,$$250,130],[4,$B to C discount fare,$$75,90],[5,$A to C full fare,$$350,140],[6,$A to C discount fare,$$125,50]]$

Find how many tickets they should allocate to each ODF to maximize revenue.

Answer:

$\backslash$table$[[$Number$,$ODF,Tickets Allocated$],[1,$A to B full fare,x$1],[2,$A to B discount fare,x$2],[3,$B to C full fare,$x3$