P$2-$A: Raw materials inventory for an oil processing plant located in Arnold, MO$,$ is procured from a large supplier via rail. Each shipment costs $$2500.$ The Arnold, MO facility produces $2,000$ gallons of oil per hour, operates $14$ hours per day in two shifts, and is open $7$ days a week for $52$ weeks a year. Raw materials cost $$0\mathrm{.}2$ per gallon and incur a holding cost of $20$ percent per year. How many gallons of raw materials should be ordered per shipment? How often will this order be placed? What is the cycle inventory for the raw materials?

P$2-$B: Consider the all$-$units quantity discount schedule below. The annual demand is $90,000$ units, the setup cost is $$1000$ per order, and the annual holding cost is $30\%$ of the unit cost. What is the optimal order quantity?

Quantity Ordered

Price Per Unit

$1499$

$$300$

$500999$

$$280$

$10001499$

$$250$

$1500$ and over

$$210$

P$3$: $(20$ points$)$: When Vidalia onions are ready, the entire $13-$county $($plus parts of seven other counties$)$ area in Georgia where they are grown is devoted to the harvest, packaging, and shipping of this delicacy. The Onion Shack currently purchases $120,000$ bags of onions each year for $$100$ per bag $($a bag is ten pounds$).$ Onion Shack has historically purchased in lots of $3000$ bags. Transit time and capacity vary as indicated in the table. The safety inventory that Onion Shack requires is $30\%$ of lead time demand and the holding cost for a bag is $15\%$ of the cost.

Carrier

Quantity Shipped $($cwt$)$

Quantity shipped $($bags$)$

Shipping cost $($$$/$cwt$)$

Transit time $($days$)$

Mashburn Rail

$200+$

$2000+$

$$2\mathrm{.}10$

$5$

Sylvia Express

$100+$

$1000+$

$$2\mathrm{.}35$

$3$

Anita Enterprises

$250+$

$2500+$

$$1\mathrm{.}35$

$3$

Smith Trucking

$250+$

$2500+$

$$1\mathrm{.}00$

$3$

Determine the least expensive transportation option if the Onion Shack continues to purchase $120,000$ bags of Vidalia onions each year.