$1.$ Formulate the problem for identifying plants and warehouse location simultaneously with quantity shipped between various plants to minimize the total costs for the network model given in

Ki is the potential capacity of factory at site i Sh is the supply capacity at supplier h

We is the warehouse capacity at site e

Fi is the Fixed cost of locating a plant at site i

Fe is the fixed cost of locating a warehouse at site e

Chi is the cost of shipping one unit from supply source h to factory i

Cie is the cost of producing and shipping one unit from factory i to warehouse e Cej is the cost of shipping one unit from warehouse e to customer j

xej is the quantity shipped from warehouse e to market j

xie is the quantity shipped from factory at site i to warehouse e xhi is the quantity shipped from supplier h to factory at site i Assume the binary variable required for the model.