A distributor sells clothing for retailers and agrees to take back the units not sold without any discount, an incentive for the retailers to order more. The market has five geographical areas, each supplied by a distribution center. There are three product lines. The decision on the quantities to order from the suppliers is based on forecasts of the final demand in each geographical area. Although the orders are aggregated for all the distribution centers, the calculations are done for each geographical area based on the forecast for that area.

Given the policy of the distributor of buying back at the same price of the units not sold, retailers order more than forecasted. Once the season begins, it is not possible to order more. When retailers are in a stockout position, the distributor tries to move products, but this process is usually without success. The movement of units between distribution centers is expensive given the distance between them:

	City 1	City 2	City 3	City 4	City
City 1	0	300	720	600	1200
City 2	300	0	900	620	1250
City 3	720	900	0	400	600
City 4	600	620	400	0	620
City 5	1200	1250	600	620	0

Given the problems with the system, the distributor is analyzing a new relationship with the retailers. The distributor will make the decisions on the quantity to be produced based on forecasts for the entire market to benefit from the consolidation effect. After deciding, they will decide how to allocate them to each distribution center. Differing from the current system, two of the distribution centers will work as central warehouses and the orders will be sent there, before allocating them to the distribution centers. The retailers will only pay at the end of the season and for the quantity they effectively sold. To analyze this new policy, the supply manager has this information:

	Line 1 - Mean	Line 1 - σ	Line 2 - Mean	Line 2 - σ	Line 3 - Mean	Line 3 - σ
City 1	2,000	1,000	3,000	1,000	800	550
City 2	2,000	920	3,500	1,050	1,200	700
City 3	3,000	1,880	4,000	1,800	1,000	600
City 4	5,000	3,000	7,500	3,100	2,000	1,400
City 5	4,000	2,420	5,000	2,300	2,500	1,315
Total	16,000	4,500	23,000	5,000	7,500	2,200

	Price	Cost	Salvage Value
Line 1	80	35	25
Line 2	15	5	4
Line 3	50	26	20

QUESTION: Compute the order quantity, per product and distribution center, under the traditional system and then choose the two distribution centers that will work as central warehouses, computing the quantity that will be allocated to each distribution center under the new policy