Problem $4($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. The costs per ton of transporting raw material from supplier to production

facility are given in the following table:

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. If you need data, variables, or constraints that are not included in

the standard minimum cost flow model, make sure you define those to make the linear programming

formulation clear.$)$

Part b: Solve the problem using an indexed model in AMPL$/$CPLEX and report the obtained optimal

solution.