Question: This Question has multiple parts I will attach an image Milford Lumber Company ships construction materials from three wood-processing plants to three retail stores. The
This Question has multiple parts I will attach an image Milford Lumber Company ships construction materials from three wood-processing plants to three retail stores. The shipping cost, monthly production capacities, and monthly demand for framing lumber are given below.
| Plant | Store A | Store B | Store C | Capacity | |||
| 1 | $4.50 | $3.10 | $2.00 | 280 | |||
| 2 | $5.10 | $2.60 | $3.80 | 460 | |||
| 3 | $4.10 | $2.90 | $4.00 | 300 | |||
| Demand | 250 | 600 | 150 |
Formulate a linear optimization model for this problem, implement your model on a spredsheet, and use Excel Solver to find a solution that minimizes total distribution costs. If the constant is equal to one, enter "1".
| Let: | |
| X11 = number of components produced in Plant 1 and supplied to Store A | |
| X12 = number of components produced in Plant 1 and supplied to Store B | |
| X13 = number of components produced in Plant 1 and supplied to Store C | |
| X21 = number of components produced in Plant 2 and supplied to Store A | |
| X22 = number of components produced in Plant 2 and supplied to Store B | |
| X23 = number of components produced in Plant 2 and supplied to Store C | |
| X31 = number of components produced in Plant 3 and supplied to Store A | |
| X32 = number of components produced in Plant 3 and supplied to Store B | |
| X33 = number of components produced in Plant 3 and supplied to Store C |
| Min | X11 | + | X12 | + | X13 | + | X21 | + | X22 | + | X23 | + | X31 | + | X32 | + | X33 | ||
| Subject to the constraints | |||||||||||||||||||
| X11 | + | X12 | + | X13 | -Select-=Item 13 | ||||||||||||||
| X21 | + | X22 | + | X23 | -Select-=Item 18 | ||||||||||||||
| X31 | + | X32 | + | X33 | -Select-=Item 23 | ||||||||||||||
| X11 | + | X21 | + | X31 | -Select-=Item 28 | ||||||||||||||
| X12 | + | X22 | + | X32 | -Select-=Item 33 | ||||||||||||||
| X13 | + | X23 | + | X33 | -Select-=Item 38 | ||||||||||||||
| X11, X12, X13, X21, X22, X23, X31, X32, X33 0 |
What is the value of total distribution costs at the optimal solution? Use the Excel solver to find the optimal solution. Round your answer to the nearest dollar.
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