A company has $2$ factories and $4$ warehouses from which it can supply the demand in $5$ customer regions. The company can fulfill customer demand by sending products to customers directly from the factories or by sending the products to the warehouses which in turn can also fulfill customer demand. The company wants to minimize the total cost of shipping its product from the factories to the warehouses, the factories to the customers, and the warehouses to the customers. How should the company distribute its products given the data below.

Each factory has the capacity of producing $60,000$ units for the planning period. The four warehouses have a capacity of $45,000,20,000,30,000,$ and $15,000$ respectively and the number of products received by a warehouse from the factory should be more than the number of products leaving the warehouse to the customer regions. The demand at the five customer regions is $30,000,23,000,15,000,32,000,$ and $16,000$ units respectively.

The table below provides the distribution cost per product from the factories to the warehouses, from factories directly to the customers, and from warehouses to customers.