Chemco operates two production facilities that manufacture achemical compound for two customers who demand $($respectively$)750$ and $840$ tons per month. Themonthly production capacity of production facility $1$ is $900$ tons and that of production facility $2$ is $730$tons. The cost per ton of compound produced is $$32$ at production facility $1$ and $$37$ at productionfacility $2.$ Raw material for the two production facilities are provided by three suppliers, who are eachcontracted to provide as much as $600$ tons of raw material at a cost of $$200/$ton $($from supplier $1),$$$208/$ton $($from supplier $2),$ and $$213/$ton $($from supplier $3).($You may assume $1$ ton of raw materialproduces $1$ ton of the compound.$)$Chemco assumes the transportation cost of both the raw material and the final compound. Rawmaterial can be transported directly from any supplier to either production facility at a per unit costgiven in the following table:ToFrom Facility $1$ Facility $2$Supplier $11013$Supplier $2815$Supplier $3149$The final compound can be transported directly from either production facility to either customer, or itcan be transported through Chemco$$s warehouse; however, the total amount of compound transportedthrough the warehouse cannot exceed $200$ tons. The costs per ton of transporting the final compoundare given in the following table:ToFrom Cust $1$ Cust $2$ WarehouseFacility $1162$Facility $2321$Warehouse $13$

$3$Part a: Formulate a minimum cost flow model to determine a minimum cost plan for transporting rawmaterial and producing and transporting compound. $($Note: For this problem, you should provide adrawing of the minimum$-$cost flow network. Explain in words what nodes and arcs represent, and labelnodes and arcs with all relevant data. You need not solve the optimization modelProblem $3($Adapted from Taha, $2003)$: Chemco operates two production facilities that manufacture a

chemical compound for two customers who demand $($respectively$)750$ and $840$ tons per month. The

monthly production capacity of production facility $1$ is $900$ tons and that of production facility $2$ is $730$

tons. The cost per ton of compound produced is $$32$ at production facility $1$ and $$37$ at production

facility $2.$ Raw material for the two production facilities are provided by three suppliers, who are each

contracted to provide as much as $600$ tons of raw material at a cost of $$(200)/()$ ton $($from supplier $1),$

$$(208)/()$ ton $($from supplier $2),$ and $$(213)/()$ ton $($from supplier $3).($You may assume $1$ ton of raw material

produces $1$ ton of the compound.$)$

Chemco assumes the transportation cost of both the raw material and the final compound. Raw

material can be transported directly from any supplier to either production facility at a per unit cost

given in the following table:

The final compound can be transported directly from either production facility to either customer, or it

can be transported through Chemco's warehouse; however, the total amount of compound transported

through the warehouse cannot exceed $200$ tons. The costs per ton of transporting the final compound

are given in the following table:

Part a: Formulate a minimum cost flow model to determine a minimum cost plan for transporting raw

material and producing and transporting compound. $($Note: For this problem, you should provide a

drawing of the minimum$-$cost flow network. Explain in words what nodes and arcs represent, and label

nodes and arcs with all relevant data. You need not solve the optimization model.$)$Problem $3($Adapted from Taha, $2003)$: Chemco operates two production facilities that manufacture a

chemical compound for two customers who demand $($respectively$)750$ and $840$ tons per month. The

monthly production capacity of production facility $1$ is $900$ tons and that of production facility $2$ is $730$

tons. The cost per ton of compound produced is $$32$ at production facility $1$ and $$37$ at production

facility $2.$ Raw material for the two production facilities are provided by three suppliers, who are each

contracted to provide as much as $600$ tons of raw material at a cost of $$\frac{200}{?}$ ton $($from supplier $1),$

$$\frac{208}{?}$ ton $($from supplier $2),$ and $$\frac{213}{?}$ ton $($from supplier $3).($You may assume $1$ ton of raw material

produces $1$ ton of the compound.$)$

Chemco assumes the transportation cost of both the raw material and the final compound. Raw

material can be transported directly from any supplier to either production facility at a per unit cost

given in the following table:

The final compound can be transported directly from either production facility to either customer, or it

can be transported through Chemco's warehouse; however, the total amount of compound transported

through the warehouse cannot exceed $200$ tons. The costs per ton of transporting the final compound

are given in the following table:

Part a: Formulate a minimum cost flow model to determine a minimum cost plan for transporting raw

materia