Assume we have $3$ locations, A$,$ B$,$ and C$,$ located on the same street. That is$,$ to go from location A to C or to go from location C to A you have to pass through location B$.$ The distance between locations A and B is $2$ miles and the distance between location B and C is $3$ miles. We also have $3$ departments. Department $1$ is responsible of producing raw material, which can then be transferred to Department $2$ responsible of processing this material to produce canned food. Canned food is then shipped to Department $3,$ which serves as a warehouse and distribution center. $1,000$ loads are shipped from Department $1$ to $2,$ and $500$ loads are shipped from Department $2$ to $3.$ Location C is the only industrial location, and hence, Department $2$ can only be placed at this location. Each truck can take one load at a time, and the same truck can be used to ship loads from one location to another, however, at the end of the day, all trucks need to return to their original location. It costs $$20/$mile to move one load. What is the optimal total transportation cost?