a$)(10$ marks$)$ Draw the inventory level of the following cases.

CGHL orders $50$ cases of yogurt whenever there are only $10$ cases left in stock. CGHL can receive their order after $5$ days.

CGHL orders ice cream every Monday. The freezer can store $10$ boxes per time but CGHL orders up to only $80\%$ of freezer capacity to lengthen its lifespan.

CGHL receives $100$ liter of fresh milk every day. Milk unsold at the end of the day is discounted for the yogurt supplier.

b$)(10$ marks$)$ Safety stock of yogurt, ice cream, fresh milk is $5$ cases, $5$ boxes and $0$ liter respectively. Calculate the average inventory level and maximum inventory level.

c$)(10$ marks$)$ Based on the data and forecast below, advice whether CGHL$$s current milk inventory policy is optimal.

Ordering cost

$$50/$ order

Demand $($bottles per day$)$

Probability

Transportation cost

$$100/$ shipment

$190$

$0\mathrm{.}25$

Unit Cost

$$10/$ liter

$200$

$0\mathrm{.}35$

Retail price

$$20/$ bottle of $500$ml

$210$

$0\mathrm{.}25$

Salvage value

$$3/$ liter unsold

$220$

$0\mathrm{.}15$