Suppose that for a given inventory situation, average annual demand is $1,000$ and the EOQ is $100.$ Demand during a lead time is random and is described by the probability distribution in table above. For a reorder point of $30$ units, determine the expected fraction of all demand that is met on time, and the expected number of cycles per year during which a shortage occurs.

MASS FUNCTION FOR LEAD TIME DEMAND

$\backslash$table$[[$Lead Time Demand,Probability$],[20,0\mathrm{.}20],[30,0\mathrm{.}20],[40,0\mathrm{.}20],[50,0\mathrm{.}20],[60,0\mathrm{.}20]]$