$($Location$-$distribution problem, reference: LN$\_$Ch$1\_04)$ Consider a supply chain network

with three potential sites for warehouses and eight retailer regions. The fixed costs $($initial

capital investment$)$ of locating warehouses at the three sites are given below:

Site $1$:$$100,000$

Site $2$: $$80,000$

Site $3$: $$110,000$

The capacities of the three sites are $100,000,80,000$ and $125,000,$ respectively. The retailer

demands are $20,000$ for the first four retailers and $25,000$ for the remaining.

The unit operating cost is not considered. The unit transportation costs $($ $ $)$ are given in the

following table.

$[$Unit transportation costs$]$

$($a$)$ Formulate the optimization problem as a linear integer program to determine the

optimal location and distribution plan that will minimize the total cost $($initial investment

transportation costs$).$ Assume dedicated warehouses, that is$,$ each retailer has to be

supplied by exactly one warehouse. You must define your variables clearly, write out the

constraints, explaining briefly the significance of each, and write the objective function.