A company purchases batches of a certain product from three suppliers (F1, F2 and F3). These batches

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Question:

A company purchases batches of a certain product from three suppliers (F1, F2 and F3). These batches are then sent to two warehouses (E1 and E2) operated by the company, then, from these warehouses, to two factories (U1 and U2) also belonging to the company. For each lot purchased, the company must pay each supplier, in addition the amount of the sale price, an amount corresponding to the cost of transport between the site the supplier and the warehouse to which the batch is sent. This transport cost depends on distance traveled. The amounts requested by each supplier, as well as the distances between supplier sites and warehouses are shown in the following table

When one of the two factories needs a certain number of batches of the product, these are routed from both warehouses. The cost of transporting a batch between each warehouse and each factory is given in the following table:

E1 E2 U1 200 $ 400 $ U2 700 $ 500 $

in addition, each supplier is able to offer up to a maximum of 10 lots per month, but can only send 6 batches per month to each warehouse. Of the same way, a maximum of 6 lots per month can be routed from each warehouse to each plant. The monthly demand at the U1 plant is 10 lots, while it is 6 lots at the U2 factory. The company wants to develop a monthly plan allowing it to determine how many lots she will have to buy from each supplier, how many lots will have to be transported between each supplier and each warehouse, and finally how many batches must be transported between each warehouse and each factory. The goal is to minimize the sum the costs of purchasing and transporting the lots.

A)Formulate this problem using a linear programming model