Question $2[25$ points$]$:

A retailer procures its required products from $4$ potential suppliers. After, the products are sent to the warehouses and then

to the stores. The company has $4$ warehouses and $4$ stores. The capacities of the suppliers and the warehouses are limited$.$

In addition, the retailer has to satisfy the demand in each store. Table $1$ shows the unit transportation cost from each

warehouse to each store, capacities of the warehouses, and the demand in each store.

Table $1$

There is a fixed monthly relationship cost to work with and manage each supplier and in order to manage the risk, we

would like to work with at least three suppliers. Table $2$ shows the unit transportation costs from each supplier to each

warehouse, the capacities of the suppliers, and the fixed cost of managing each supplier.

Table $2$

Find the optimal transportation quantity from each supplier to each warehouse, and from each warehouse to each store.

Which suppliers should be used?