Please explain the anwsers that are already provided. Annual demand for a particular halogen bulb $12,000$ at a business that operates $240$ days per year. The calculated EOQ is $400$ bulbs. The lead time from the supplier of the bulbs is $12$ working days.

a$)[4$ points$]$ When the lead time demand is constant, what is the reorder point?

Lead time demand $=12\frac{12000}{240}=600$

ROP$=$ Remainder of $\frac{600}{400},200$

Now assume that the demand during lead time follows the empirical distribution in the following table:

$\backslash$table$[[$Demand$,$Probability$],[100,0\mathrm{.}05],[150,0\mathrm{.}10],[200,0\mathrm{.}20],[250,0\mathrm{.}30],[300,0\mathrm{.}20],[350,0\mathrm{.}10],[400,0\mathrm{.}05]]$

$[4$ points$]$ What is the service level when the safety stock is $100?95\%\_.1-05($average demand$=$lead time demand$)$

$[4$ points$]$ What is the probability of a stock out $($i$.$e probability of not meeting demand$)$ when the ROP is $300?(1-0\mathrm{.}85)$ E because $350$ and $400$ are above $15$

$[4$ points$]$ For a service level of $$5\%,$ what should the safety Wok be$?$