Jacobs Manufacturing produces a popular custom accessory for pickup trucks at plants in Huntington, West Virginia and Bakersfield, California, and ships them to distributors in Dallas, Texas; Chicago, Illinois; Denver, Colorado; and Atlanta, Georgia. The plants in Huntington and Bakersfield have, respectively, the capacity to produce 3,000 and 4,000 units per month. For the month of October, costs of shipping a carton of 10 units from each plant to each distributor are summarized in the following table:
Jacobs has been notified that these shipping rates will each increase by $1.50 on November 1. Each distributor has ordered 1,500 units of Jacobs’ product for October and 2,000 units for November. In any month, Jacobs can send each distributor up to 500 units more than they have ordered if Jacobs provides a $2 per unit discount on the excess (which the distributor must hold in inventory from one month to the next). In October, the per unit cost of production in Huntington and Bakersfield are $12 and $16, respectively. In November, Jacobs expects the cost of production at both plants to be $14 per unit. The company wants to develop production and distribution plan for the months of October and November that would allow them to meet the expected demand from each distributor at the minimum cost. a. Draw a network flow model for this problem. b. Implement your model in a spreadsheet and solve it. c. What is the optimalsolution?
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