R&T Whoselares distributes general merchandise to retailers across India. There are numerous warehouses located throughout the country that serve as points of sale and warehouses for delivery vehicles that serve retailers in the cities surrounding the warehouses. The warehouse serving the districts of Prakasam, Guntur, Krishna, West Godavari and East Godavari is located in Vijayawada. Delivery volume is represented in terms of average sales activity per city visit, which groups stops at a number of retailers within each city. From a map of the warehouse region (the table), linear coordinates are constructed for the warehouse and for each city. The coordinates have a scale factor on the map of 1 coordinate unit = 12.3 kilometers. The circuit factor that converts computer-coordinated distances to road distances is 1.12. The capacity of the vehicles is 500000 in terms of sales. Determine the minimum routes that guarantee compliance with the volumes at each of the points.

Number	X	Y	Sales per visit
0	19.4	15.1	0
1	14.5	5.3	66000
2	10.7	7	24000
3	14.5	6.2	305000
4	7.7	8.2	60000
5	9.6	5.1	24000
6	13.2	3.5	90000
7	3.8	5	25000
8	17.2	9	98000
9	6.3	6.3	25000
10	13.9	8.8	60000
11	15.4	11.4	92000
12	14.5	12.5	100000
13	11.8	11	65000
14	18.1	14.3	60000
15	15.2	14	45000
16	21.3	10.6	50000
17	18	13	450000
18	21.3	13.6	39000
19	19.7	12.5	140000
20	22.3	13.2	62000
21	21.3	17.5	37000
22	23.8	12	108000
23	24.4	15.5	48000
24	14.9	18.5	37000
25	19.5	15.2	50000
26	22.7	14.3	180000
27	18.2	9.7	82000
28	29.5	19.6	470000
29	30.8	18.3	170000
30	28.7	14.5	160000

Establish the objective function and restrictions.