Operations Research question, maybe it is a network flow problem or dynamic problem or a transport problem.

 A cement producing company meets the demand of a country composed of 10 consumer regions, designated as R1,R2,...,R10, which are interconnected by the road system shown in the figure below.

The annual demands of these consumer regions are shown in table 1. In this region, the company has four factories, whose location, production costs and annual capacities are shown in table 2. answer: *formulate the model for the problem presented; *what kind of technique would you use to solve this problem.

Data:

*Unit cost of transport: $ 0,23 per ton.km

Region	current demand (1000 ton)
R1	500
R2	350
R3	610
R4	470
R5	290
R6	520
R7	180
R8	350
R9	270
R10	710
Total	4250
transport cost	0,23	ton*Km

Table 1

Factory	Factory location	Annual production capacity (1000 ton)	production cost($/ ton)	total cost (1000 ton)
FA	R1	920	480	441600
FB	R4	1150	570	655500
FC	R10	1220	280	341600
FD	R6	1370	530	726100

table 2

R6 R2 R9 4 400 km ( 430 km - R1 ( 300 km 270 km 4270 km R4 610 km R8 ( 410 km) (250 km 150 km R3 560 km) R7 R10 (230 km - R5 R6 R2 R9 4 400 km ( 430 km - R1 ( 300 km 270 km 4270 km R4 610 km R8 ( 410 km) (250 km 150 km R3 560 km) R7 R10 (230 km - R5