Problem $3(2\mathrm{.}5$ pts$)$ A hotel numbers its fare classes from higher to lower as $1,2,3$ and $4.$ The room prices for these classes are p$1=$$$300,$ p$2=$$$250,$ p$3=$$$200,$ p$4=$$$150.$ The demands for these fare classes are denoted by D$1,$ D$2,$ D$3$ and D$4.$ The hotel considers the cumulative demands

D$1=$ D$1,$ D$1,2=$ D$1+$ D$2,$ D$1,2,3=$ D$1+$ D$2+$ D$3,$ D$1,2,3,4=$ D$1+$ D$2+$ D$3+$ D$4.$

These demands turn out to have uniform distributions with the following ranges:

D$1$ in $[0,10],$ D$1,2$ in $[0,20],$ D$1,2,3$ in $[0,30],$ D$1,2,3,4$ in $[0,40].$

a$)(0\mathrm{.}5$ pts$)$ Before applying EMSR$-$b heuristic, the hotel needs aggregate prices p$1,$ p$1,2,$ p$1,2,3$ and p$1,2,3,4.$ Compute these prices.

b$)(0\mathrm{.}5$ pts$)$ What is the protection level y$3$ for classes $\{1,2,3\}?$

c$)(0\mathrm{.}5$ pts$)$ What is the protection level y$2$ for classes $\{1,2\}?$

d$)(0\mathrm{.}5$ pts$)$ What is the protection level y$1$ for class $\{1\}?$

e$)(0\mathrm{.}5$ pts$)$ How does protection level y$1$ change when p$3$ reduces to $$160?$