An airline has fare classes from higher to lower as $1,2$ and $3.$ The airline has $200$ seats. The ticket prices for the classes are $p_1=$$$500,p_2=$$$400,p_3=$$$300.$ The uniformly distributed demands for these fare classes are denoted by $D_1,D_2$ and $D_3$ :

$D_{1}in[0,40],$

$D_{2}in[0,96],$

$D_{3}in[0,400].$

The airline applies EMSR$-$a heuristic to find the protection levels for classes.

a$)$ Find the protection level $y_2.$

b$)$ What is the booking limit b $b_3$ for the third class?

c$)$ Find $y_{1,2}.$