A newsstand operator assigns probabilities to the demand for Fine magazine: $.$

Event: Demand

$10$ copies $11$ copies $12$ copies $13$ copies $14$ copies

Probability of Event

$0\mathrm{.}100\mathrm{.}150\mathrm{.}200\mathrm{.}250\mathrm{.}351\mathrm{.}00$

Issues sell for $50$ cents and cost $30$ cents.

a$.$ If the operator can return and cost $30$ cents.

b$.$ If the operator cannot return any unsold copies for full credit, how many should be ordered?

c$.$ What is the optimum expected profit in $($b$)?$