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Question $5$: 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 the below table $($two suppliers offer quantity discounts$).$

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. Solve using any IP software $($Lindo$,$ Excel Solver etc.$).$ Attach the computer output containing the optimal solution. Explain the optimal solution in words.

$(15$ points$)$

Supplier Fixed Cost Capacity Unit Price $1$ $$100600$ units

$$10//$ unit for the first $300$ units $$7//$ unit for the remaining $300$ units $$2//$ unit for all $800$ units

$2$ $$500800$ units

$$6//$ unit for the first $500$ units $$4/$unit for the remaining $700$ units