This network optimization problem is a Minimum Cost Flow problem. The goal is to find the flow (production quantities) from the source to the sink while minimizing the total cost, which includes production costs and inventory carrying costs.

Mathematically formulate the corresponding network optimization problem from the above information. To do so, clearly define the decision variables, and then formulate the algebraic model using your decision variables.

Nodes: 1 Node S (Source) 2 . Node 1 (Month 1 production) 3 . Node 2 (Month 2 production) 4 Node T (Sink) Arcs: 1 . From S to Node 1 with a capacity of 75 units and a cost of $10 per unit. 2 . From S to Node 2 with a capacity of 75 units and a cost of $15 per unit. 3 . From Node 1 to Node 2 with a capacity of 50 units and a cost of $5 perunit (inventory carrying cost). 4. From Node 1 to T with a capacity of 75 units and no cost (demand satisfaction). 5 . From Node 2 to T with a capacity of 80 units and no cost (demand satisfaction)