Curly Hair is a Brazilian start-up that offers a wide portfolioof hair products (shampoo, conditioner, foam, serum…) specificallydesigned to take care of curly hair.

Curly Hair manufactures its products in three different plantsand sells them in five markets around the country. The plants havea certain manufacturing capacity. In the tables below, you can findthe demand for each market, the capacity of each plant, and thedistances (in miles) between plants and markets.

Demand per market (in liters)
M1	375
M2	230
M3	229
M4	246
M5	383

Plant capacity (in liters)
P1	510
P2	700
P3	620

Distance from plants to markets (in miles)
	M1	M2	M3	M4	M5
P1	28	22	21	38	44
P2	16	42	11	14	35
P3	24	45	42	31	49

The operations manager of the company proposes to redesign thetransportation network and start using some distribution centers(DCs) as an intermediary step between plants and final markets.There are four DCs that could be used. These DCs have a certaincapacity and they cannot be used as warehouses (they do not keepstock), products must just flow through them.

In the tables below you will find the maximum capacity of eachDCs, the distances between plants and DCs, and the distancesbetween DC and markets.

Capacity of each DC (in liters)
DC1	900
DC2	650
DC3	850
DC4	1000

Distance from plants to DCs (in miles)
	DC1	DC2	DC3	DC4
P1	53	20	36	24
P2	47	19	37	60
P3	59	29	14	52

Distance from DCs to markets (in miles)
	M1	M2	M3	M4	M5
DC1	21	31	26	17	27
DC2	28	12	27	43	39
DC3	22	49	16	39	50
DC4	25	45	44	47	18

The inbound transportation cost (from plants to DCs) is 2.61Brazilian reals per liter per mile, and the outbound transportationcost (from DCs to markets) is 3.02 Brazilian reals per liter permile. There is also a fixed cost of 5,000 Brazilian reals for eachDC that the company decides to use.

Design a distribution network that can use these DCs. What isthe optimal cost (transportation + fixed cost) under this newsituation?