Jones company has two manufacturing plants A and B, and three warehouses, W1, W2, W3. Each...
Jones company has two manufacturing plants A and B, and three warehouses, W1, W2, W3. Each week Jones ships product from the plants to the warehouses. The system is balanced: A produces 500 units of product and B produces 300 units of product. Warehouse W1 needs 200 units of product, W2 needs 300 units of product, and W3 needs 300 units of product. Thus, over the entire system, there are 800 units produced by the two plants and 800 units received by the three warehouses.
The cost of shipping from the plants to the warehouses is given by the following chart, where the numbers in the cells give the cost in collars to ship one unit from the plant to the warehouse.
| Warehouse | ||||
| W1 | W2 | W3 | ||
| Plants | A | 5 | 10 | 6 |
| B | 8 | 5 | 6 |
Jones wants to minimize total shipping costs. How much should Jones ship from each manufacturing plant to each warehouse in order to minimize cost? What will the cost be?
a. Set this problem up as a linear programming problem
b. Solve using a computer program and give the values of the decision variables and the objective function for your solution.
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