A product has a reorder point of $110$ units and is ordered four times a

year on average. The following table shows the historical distribution of

demand values observed during lead time.

Demand Probability.

$100$

$\mathrm{.}3$

$110$

$\mathrm{.}3$

$120$

$\mathrm{.}2$

$130$

$\mathrm{.}2$

Managers have noted that stockouts occur $30$ percent of the time with

this policy, and they question whether a change in inventory policy, to

include some safety stock, might be an improvement. The managers

realize that any safety stock would increase the service level, but they

are worried about the increased costs of carrying the safety stock.

Currently, stockouts are valued at $$20$ per unit per occurrence, while

inventory carrying costs are $$10$ per unit per year.

A$.$ What is the sum of additional holding cost and stockout cost when

ROP is $110($i$.$e$.,$ in case of zero safety stock$)?$

B$.$ What is the sum of additional holding cost and stockout cost when

ROP is $120($i$.$e$.,$ in case of $10$ units of safety stock$)?$

C$.$ What level of safety stock is best?