Question
Jack's Small Enterprises runs two factories in Ohio: one in Toledo and one in Centerville. Its factories produce a variety of products. Two of its
Jack's Small Enterprises runs two factories in Ohio: one in Toledo and one in Centerville. Its factories produce a variety of products. Two of its product lines are polished wood clocks, which are adorned with a regional theme. Naturally, clocks popular in the southwest are not as popular in the northeast, and vice versa. Each plant makes both clocks. These clocks are shipped to St Louis for distribution to the southeast and western states and to Pittsburgh for distribution to the south and northeast states. The company is considering streamlining its plants by removing certain production lines from certain plants. The company could potentially eliminate the clock production line at either the Toledo or the Centerville plant. Each plant carries a fixed operating cost for setting up the line and a unit production cost, both in terms of money and factory worker hours. The following table summarizes this information:
Production Cost | Clocks Produced | |||||
per Clock | per Hour | Available | ||||
Plant | Fixed Cost for | Southwest | Northeast | Southwest | Northwest | Hours per |
Line | Clock | Clock | Clock | Clock | Month | |
Toledo | $20,000 | $10 | $12 | 5 | 6 | 500 |
Centerville | $24,000 | $9 | $13 | 5.5 | 6.2 | 675 |
The southwest clocks are sold for $23 each, and the northeast clocks are sold for $25 each. Demand rates used for production planning are 1,875 southwest clocks for sale out of the St Louis distribution center and 2,000 northeast clocks for sale out of the Pittsburgh distribution center. Assume all these units are sold. The per-clock transportation costs from plant to distribution center are given in the following table:
Cost to Ship to Distribution Center | ||
Plant | St Louis | Pittsburgh |
Toledo | $2 | $4 |
Centerville | 3 | 2 |
Using a network flow model for this problem and implement this model in Solver. Use the model to answer the following questions:
a. | Should any of the production lines be shut down? |
b. | How should worker hours be allocated to produce the clocks to meet the demand forecasts? Are there any excess hours? If so, how many? |
c. | What is the expected monthly profit? |
d. | If a plant is closed, what are the estimated monthly savings? |
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