PLEASE MAKE SURE YOU USE Xij as the desicion variable! LOOK AT THE HINT! Just fo

Question

PLEASE MAKE SURE YOU USE Xij as the desicion variable! LOOK AT THE HINT!

Just formulate the model to this problem. Do not solve this problem. Singher Cola is one of the most successful cola companies in Asia. The first Singher Cola was produced in 1933, and since then, it has been exported to 50 countries worldwide. The cola is still a top seller in Thailand, and in one of its main distribution centers, a manager has been presented with a linear programming problem. One of the Singher factories in the northern part of Bangkok supplies four different small villages from three of its plants, and the unitary cost of each box for shipment (in USS) is presented in the table below. There are other constraints that need to be considered when formulating the linear programming problem. Not all plants are able to supply the same quantity of cola required. According to the last estimation, Plant A can supply a maximum of 35 per day, Plant B can supply 50, and Plant C can supply 40. However, city A needs at least 45 every day, City B needs 20, and Cities C and D need 30 to fulfill demand. Therefore, the manager has to combine the production from the three plants to satisfy the demand while still keeping a reasonable shipping price. Determine a suitable linear programming model that can address the issue and create its parameter table.

Explanation / Answer

Decision Variables:

Xij represents quantity of product shipped from Plant i (=A,B,C) to City j (=A,B,C,D)

Objective function:

Minimize total cost of shipment: z = CijXij, where Cij is the unitary cost of each box for shipment from Plant i (=A,B,C) to City j (=A,B,C,D)

Constraints:

Xij (i = A, j = A,B,C,D) 35

Xij (i = B, j = A,B,C,D) 50

Xij (i = C, j = A,B,C,D) 40

Xij (i = A,B,C, j = A) 45

Xij (i = A,B,C, j = B) 20

Xij (i = A,B,C, j = C) 30

Xij (i = A,B,C, j = D) 30

Xij 0

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