A manager must set up inventory ordering systems for two new items, Gadget and Widget. Gadget is ordered frone supplies and is delivered at once, while Wayston proticed nehouse in batches of fixed size. Sales are done via the company's website $24/7$ all$-$year round, wider snoor each rem is normally distributed. The company uses a continuous inventory system. The manager has gathered the following information about the items,

Widget

Gadget

$100$ units per day.

Average demand

$12,000$ units per year

Standard deviation $($or$)$

$50$ units per week

$20$ units per week

$$400$

Unit cost $($Cu$).$

$$33.$

$500$ units per day

Production rate $($Pi$)$

$15\%$

Annual carrying cost rate $($i$).$

$20\%$

$$10,520$

Ordering cost or setup cost $($C$.)$

$$2500$

$7$ days

Lead time $($L$.)$

$3$ weeks

Service level desired $($a$)$

$99\mathrm{.}9\%$

$97\mathrm{.}5\%$

Compute the optimal order quantity for Gadget.

How many orders of item Gadget will be placed per year?

What should the safety stock be for Gadget to ensure the desired level of service?

What is the time between two consecutive orders of Gadget, in weeks?

Compute the optimal order quantity for Widget. How many orders will be placed per year?

When should the manager reorder item Widget to achieve the desired level of service?

How long will take to produce each production run $($each batch$)$ of item Widget, in days?

What will be the maximum level $($H$)$ of inventory of Widget?