Question $2$: $(5$ points$)$ Inventory Management $($Single Period Inventory Model$)$

Newspaper Boy Problem: Daily demand for a newspaper is independent and identical. Demand can be characterized as the following probability distribution:

$\backslash$table$[[$Demand in units,Probability$],[10,0\mathrm{.}2],[20,0\mathrm{.}2],[30,0\mathrm{.}2],[40,0\mathrm{.}2],[50,0\mathrm{.}2]]$

The cost of the newspaper is $$1.$ The newspaper is sold to customers for a price of $$1\mathrm{.}40$ each. At the end of the day, any unsold newspapers have to be returned to the publisher and yield a revenue of $$0\mathrm{.}25$ per copy.

A$)$ How many newspapers will be optimal to be inventoried at the start of the day, so the expected profit is maximum?

B$)$ What are the expected $($average$)$ profits for each stock $($inventory$)$ level? Simulate for $15$ days and draw your conclusions. Use only the random numbers provided to generate demand.