A toy store chain operates $100$ retail stores throughout the United States. The company currently ships

all products from a central distribution center $($DC$)$ to the stores, but it is considering closing

the central DC and instead operating multiple regional DCs that serve the retail stores. It

will use the UFLP to determine where to locate DCs$.$ Planners at the company have identified $24$ potential cities in which regional DCs may be located. The file toy$-$stores.xlsx

lists the longitude and latitude for all of the locations $($stores and DCs$),$ as well as the

annual demand $($measured in pallets$)$ at each store and the fixed annual location cost at

each potential DC location. Assume that transportation from DCs to stores costs $$1$ per

mile, as measured by the great circle distance between the two locations. In this problem, you will implement the Lagrangian Relaxation algorithm. We provide a code template

$($solve with LR template.ipynb$),$ but you are free to use any programming languages.