Scenario $11\mathrm{.}1-$ Bubble and Squeak

The rising popularity of bubble and squeak as a breakfast item on the menu has resulted in a steady demand for peas. Over the course of the past week, $455$ patrons have ordered the hearty breakfast and each serving contains a$$half cup$$of English peas. It costs two cents to hold a$$half cup$$of peas in inventory for a year and $$5$ to place an order $($remember they come all the way from England!$).$ It takes $2$ weeks to ship a container from England loaded with peas.

$1.$ What is the optimal order quantity for peas, in half$-$cups?

What is the average inventory, in half cups of peas, if they order at the optimal order quantity and don't hold any safety stock?

$.$How many orders per year does the diner place if they order at the economic order quantity $($round UP to nearest whole order$)?$

What is the average flow time, in whole days, of a half cup of peas if the diner orders at the economic order quantity?

The diner orders at the economic order quantity and carries no safety inventory, so$$ordering and holding costs are the only inventory costs. $$ What is the cost of this inventory policy $($excluding cost of goods$),$ in whole dollars?

The diner has an inventory system that calculates optimal order quantity using the EOQ. An analysis of dates on the cans of peas revealed that the flow time wasn't what the diner expected. This led to a quick inventory policy check which revealed that the computer had automatically adjusted the economic order quantity to $3,123$half cups$$as demand had changed during the past few months. This order quantity is automatically calculated using the EOQ. Using this information, what is the current weekly demand for English peas in half cups?

The diner typically orders at the economic order quantity, however, the new kitchen manager is a little nervous about running out of peas, so she decided to$$double the size of pea orders. The diner still carries no safety inventory $($sounds like the manager needs some basic inventory management education!$)$ so$$ordering and holding costs are the only inventory costs. $$ How much additional inventory cost does the diner incur by ordering double the EOQ instead of just following the policy of order size being equal to the EOQ? Exclude the cost of goods and answer in whole dollars.

The rising popularity of bubble and squeak as a breakfast item on the menu has resulted in a steady demand for peas. Over the course of the past week, $448$ patrons have ordered the hearty breakfast and each serving contains a half cup of English peas. It costs two cents to hold a half cup of peas in inventory for a year and $$4$ to place an order $($remember they come all the way from England!$).$ It takes $6$ weeks to ship a container from England loaded with peas. $$ What is the lead time for an order of peas, in weeks?