HighMed, a manufacturer of medical equipment used in heart procedure, is located in Madison,

Wisconsin. The medical equipment is sold directly to cardiologists all over North America.

HighMed currently divides the United States into $24$ territories, each with its own sales force. All

product inventories are maintained locally in each territory and replenished from Madison every

four weeks using UPS. The average replenishment time using UPS is one week. UPS charges

$$0\mathrm{.}66+0\mathrm{.}26$x where x is the quantity shipped in pounds. The products sold fall in two categories $$

High value and Low value. High value products weigh $0\mathrm{.}1$ pounds and cost $$200$ each while Low

value products weigh $0\mathrm{.}04$ pounds and cost $$30$ each.

Weekly demand for High value products in each territory is normally distributed, with a mean of

$2$ and a standard deviation of $5.$ Weekly demand for Low value products in each territory is also

normally distributed with a mean of $20$ and a standard deviation of $5.$ HighMed maintains sufficient

safety inventories in each territory to provide a cycle service level of $0\mathrm{.}997$ for each product.

Annual holding cost at HighMed is $25\%.$

The management team at HighMed is contemplating the following option:

$$Eliminate inventories in the territories, aggregate all inventories in a finished goods warehouse at

Madison and replenish the warehouse once a week$.$

If inventories are aggregated at Madison, orders will be shipped using FedEx, which charges

$$5\mathrm{.}53+0\mathrm{.}53$x per shipment, where x is the quantity shipped in pounds. The factory requires a one

week lead time to replenish finished goods inventories at Madison warehouse. An average

customer order is for $1$ unit of High value and $10$ units of Low value items. What should HighMed

do$?$