A logistics specialist for Charm City Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

Assembly Plant

1 2 3 Supply

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A 6, 10, 14, 200

Factory B 2, 2, 6, 400

C 2, 8, 7, 200

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Demand 220, 320, 200

The specialist wants to distribute at least 100 cases of parts from factory B to assembly plant 2.

(a) Formulate a linear programming problem to minimize total cost for this transportation problem.

(b) Solve the linear programming formulation from part (a) by using either Excel or QM for Windows. Find and interpret the optimal solution and optimal value. Please also include the computer output with your submission.

The following questions are mathematical modeling questions. Please answer by defining decision variables, objective function, and all the constraints. Write all details of the formulation. Please do NOT solve the problems after formulating.