Goutte is a Canadian company manufacturing and distributing soft drinks Manufacturing plants are used to satisfy the demand of sales districts The production process makes use of water, available anywhere in Canada in an unlimited quantity at a negligible cost, and of sugar extracts which compose a modest percentage of the total weight of the finished product For this reason, supply costs are negligible compared to finished product distribution costs The management would like to determine the plant configuration that minimizes the sum of weighted transportation costs and fixed facility opening costs The maximum acceptable distance between a potential plant and a sales district is 75 km Demand can be split among facilities The fixed costs and capacities of potential plant locations are given in Table 1 and sales district demands are given in Table 2 Table 3 provides per truckload transportation costs between potential plants and sales districts, and Table 4 provides distances Draw a graph (network representation) of this logistics network, where the potential plant locations and sales districts form the nodes of the network and arcs represent available connections between the nodes Formulate a mixed integer program appropriate for this problem and include it in your homework submission This should be written using the type of math modeling notation we use in the lecture PPT (e g , d i c ij X ij ) not in Excel Implement and solve this model in Excel, provide a graphical representation of the solution (similar to how we have depicted solutions in class) Note that because demand can be split among plants if needed, the edges in your graph should be labeled with decision variable values representing the fraction of demand from a sales district that has been assigned to a particular plant Table 1 Fixed costs and capacities of potential plant locations Potential plant location Fixed cost ($) Capacity (hectolitres) Brossard 81,400 22,000 Granby 83,800 24,000 LaSalle 88,600 28,000 Mascouche 91,000 30,000 Montreal 79,000 20,000 Sainte Julie 86,200 26,000 Sherbrooke 88,600 28,000 Terrebonne 91,000 30,000 Valleyfield 79,000 20,000 Verdun 80,200 21,000 Table 2 Demands of sales districts Sales district Demand (hectolitres) Demand (truckloads) Brossard 14,000 94 Granby 10,000 67 Sainte Julie 8,000 54 Sherbrooke 12,000 80 Valleyfield 10,000 67 Verdun 9,000 60 Table 3 Per truckload transportation costs Brossard Granby Sainte Julie Sher brooke Valley field Verdun Brossard 0 140 02 55 94 256 50 133 58 21 53 Granby 140 02 0 130 64 142 05 265 88 154 01 LaSalle 38 27 170 94 86 85 287 22 87 40 21 53 Mascouche 100 65 208 47 97 34 344 45 171 12 83 17 Montreal 24 84 157 32 51 52 273 61 123 83 17 11 Sainte Julie 55 94 130 64 0 254 29 173 88 70 10 Sherbrooke 256 50 142 05 254 29 0 382 54 270 30 Terrebonne 87 95 195 96 85 01 331 57 159 53 71 58 Valleyfield 133 58 265 88 173 88 382 54 0 116 66 Verdun 21 53 154 01 70 10 270 30 116 66 0 Table 4 Distances Brossard Granby Sainte Julie Sher brooke Valley field Verdun Brossard 0 76 1 30 4 139 4 72 6 11 7 Granby 76 1 0 71 77 2 144 5 83 7 LaSalle 20 8 92 9 47 2 156 1 47 5 11 7 Mascouche 54 7 113 3 52 9 187 2 93 45 2 Montreal 13 5 85 5 28 148 7 67 3 9 3 Sainte Julie 30 4 71 0 138 2 94 5 38 1 Sherbrooke 139 4 77 2 138 2 0 207 9 146 9 Terrebonne 47 8 106 5 46 2 180 2 86 7 38 9 Valleyfield 72 6 144 5 94 5 207 9 0 63 4 Verdun 11 7 83 7 38 1 146 9 63 4 0 Need help answering these

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Goutte is a Canadian company manufacturing and distributing soft drinks. Manufacturing plants are used to satisfy the demand of sales districts. The production process makes

Goutte is a Canadian company manufacturing and distributing soft drinks. Manufacturing plants are used to satisfy the demand of sales districts. The production process makes use of water, available anywhere in Canada in an unlimited quantity at a negligible cost, and of sugar extracts which compose a modest percentage of the total weight of the finished product. For this reason, supply costs are negligible compared to finished product distribution costs. The management would like to determine the plant configuration that minimizes the sum of weighted transportation costs and fixed facility opening costs. The maximum acceptable distance between a potential plant and a sales district is 75 km. Demand can be split among facilities. The fixed costs and capacities of potential plant locations are given in Table 1 and sales district demands are given in Table 2. Table 3 provides per-truckload-transportation costs between potential plants and sales districts, and Table 4 provides distances.

Draw a graph (network representation) of this logistics network, where the potential plant locations and sales districts form the nodes of the network and arcs represent available connections between the nodes.
Formulate a mixed integer program appropriate for this problem and include it in your homework submission. This should be written using the type of math modeling notation we use in the lecture PPT (e.g., d_ic_ijX_ij); not in Excel.
Implement and solve this model in Excel, provide a graphical representation of the solution (similar to how we have depicted solutions in class). Note that because demand can be split among plants if needed, the edges in your graph should be labeled with decision variable values representing the fraction of demand from a sales district that has been assigned to a particular plant.

Table 1: Fixed costs and capacities of potential plant locations

Potential plant location	Fixed cost ($)	Capacity (hectolitres)
Brossard	81,400	22,000
Granby	83,800	24,000
LaSalle	88,600	28,000
Mascouche	91,000	30,000
Montreal	79,000	20,000
Sainte-Julie	86,200	26,000
Sherbrooke	88,600	28,000
Terrebonne	91,000	30,000
Valleyfield	79,000	20,000
Verdun	80,200	21,000

Table 2: Demands of sales districts

Sales district	Demand (hectolitres)	Demand (truckloads)
Brossard	14,000	94
Granby	10,000	67
Sainte-Julie	8,000	54
Sherbrooke	12,000	80
Valleyfield	10,000	67
Verdun	9,000	60

Table 3: Per-truckload transportation costs

	Brossard	Granby	Sainte- Julie	Sher-brooke	Valley-field	Verdun
Brossard	0	140.02	55.94	256.50	133.58	21.53
Granby	140.02	0	130.64	142.05	265.88	154.01
LaSalle	38.27	170.94	86.85	287.22	87.40	21.53
Mascouche	100.65	208.47	97.34	344.45	171.12	83.17
Montreal	24.84	157.32	51.52	273.61	123.83	17.11
Sainte-Julie	55.94	130.64	0	254.29	173.88	70.10
Sherbrooke	256.50	142.05	254.29	0	382.54	270.30
Terrebonne	87.95	195.96	85.01	331.57	159.53	71.58
Valleyfield	133.58	265.88	173.88	382.54	0	116.66
Verdun	21.53	154.01	70.10	270.30	116.66	0

Table 4: Distances

	Brossard	Granby	Sainte- Julie	Sher-brooke	Valley-field	Verdun
Brossard	0	76.1	30.4	139.4	72.6	11.7
Granby	76.1	0	71	77.2	144.5	83.7
LaSalle	20.8	92.9	47.2	156.1	47.5	11.7
Mascouche	54.7	113.3	52.9	187.2	93	45.2
Montreal	13.5	85.5	28	148.7	67.3	9.3
Sainte-Julie	30.4	71	0	138.2	94.5	38.1
Sherbrooke	139.4	77.2	138.2	0	207.9	146.9
Terrebonne	47.8	106.5	46.2	180.2	86.7	38.9
Valleyfield	72.6	144.5	94.5	207.9	0	63.4
Verdun	11.7	83.7	38.1	146.9	63.4	0