Consider a supplier order allocation problem under multiple sourcing, where it is required to buy 2000 units of a certain product from three different suppliers. The fixed set-up cost (independent of the order quantity), variable cost (unit price), and the maximum capacity of each supplier are given in Table below (two suppliers offer quantity discounts). Supplier Fixed cost Capacity Unit Price 1 $100 600 units $10/unit for the first 300 units $7/unit for the remaining 300 units 2 $500 800 units $2/unit for all 800 units 3 $300 1200 units $6/unit for the first 500 units $4/unit for the remaining 700 units The objective is to minimize the total cost of purchasing (fixed plus variable cost). Formulate this as a linear integer programming problem. You must define all your variables clearly, write out the constraints to be satisfied with a brief explanation of each and develop the objective function. Reformulate the above problem under the assumption that both suppliers 1 and 3 offer "all units" discount, as described in the following: Supplier 1 charges $10/unit for orders up to 300 units and for orders more than 300 units, the entire order will be priced at $7/unit. Supplier 3 charges $6/unit for orders up to 500 units and for orders more than 500 units, the entire order is priced at $4/unit