Problem $3(25)$: A supply chain for ABC company consists of three plants, two

intermediate warehouses, and three retail stores. Plant capacities and shipping costs

per unit from each plant to each warehouse are listed in the following table.

Table $1$: Shipping cost $($$$/$unit$)$ Plant to Warehouse and Plant capacity

Shipping costs from each warehouse to each final destination retail store and

store demand are listed in the following table

Table $2$: Shipping cost $($$$/$unit$)$ Plant to Warehouse and Retail Store Demand

The operation manager wishes to determine the minimum$-$cost shipping plan from

each plant to warehouse and from each warehouse to final retail store.

Develop a network diagram of the above problem. Label all arcs, nodes,

supply, and demand $(5)$

Formulate the above problem as a linear program. Clearly define the decision

variables, objective function, and constraints. General mathematical

expressions are acceptable. $(10)$

a$.$ Decision Variables:

b$.$ Objective Function:

c$.$ Constraints:

Solve the problem using Excel Solver. You must provide screen shots of the

solver model and solution in Excel to receive credit. Clearly identify the

optimal shipping plan and total cost. $(10)$