Question $5)$

Cool Summer is a beverage company. It has $20$ distribution centers located in different states to supply its $500$ retail partners. Each retail partner $j$ has a weekly demand level of $d_j.$ Shipping cost per bottle of beverage from distribution center $i$ to retail store $j$ is $c_{ij}.$ Once it is decided to ship from distribution center $i$ to retail store $j,$ a labor cost of $f_i$ is incurred. Find the minimum cost shipping plan so that demand from each retail partner is satisfied. $($Fixed Charge Transportation$)20$ points