uppose that a manager needs to order a component

to satisfy next week$$s demand. The probability that there will be x $($integer$)$

units of demand is $1/20$ where $10<$ x $<=30.$

The manager can pay $$1$ per unit to order some components from a regular

channel in advance. If it turns out that the amount is not sufficient to satisfy

all demands, the manager needs to place an expediting orders at $$1\mathrm{.}8$ per unit to

cover the shortage. Unused component can be sold in the second$-$hand market

at $$0\mathrm{.}3$ per unit. Determine

$1.(8$ points$)$ The optimal number of units that the manager should order

from the regular channel;

$2.(4$ points$)$ The expected number of units of expediting orders;

$3.(4$ points$)$ The expected total purchase cost $($include both regular and

expediting orders$)$;

$4.(4$ points$)$ The expected salvage value of unused units sold in the second$-$

hand market