A lumber company produces premium mahogany hardwood for flooring in three plants and ships them to four sales areas. The three supply plants are located in Raleigh, Peoria, and Columbus. The four demand destinations are located in Atlanta, Buffalo, Chicago, and Denver. The fixed supply and demand in each market are expressed in units of tons. The unit transportation costs, fixed supply for each plant, and fixed demand for each sales area are summarized below:
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Supply Regions
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Raleigh (R)
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Peoria (P)
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Columbus (C)
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Demand
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($/ton)
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Atlanta (A)
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200
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500
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400
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13
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Buffalo (B)
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450
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350
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250
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7
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Chicago (C)
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600
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150
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250
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15
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Denver (D)
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900
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500
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600
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10
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Supply
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25
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15
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10
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a. Determine the least-cost method of distribution for the firm.
b. Make a map of this problem and fill in the optimal shipments in the map.
c. What is the optimal number of shipments that should be made from the plant at Raleigh?
d. How many units should be shipped from Peoria to Buffalo?
e. How much would costs be reduced in the optimal solution if additional lumber were produced at the Peoria plant?
f. If demand in Atlanta were increased by three units, how much would the objec- tive function value in the optimal solution increase?
g. How much can the cost of shipping from Raleigh to Atlanta increase before a new optimal solution is required? How much could this cost decrease?
h. How much must the cost of shipping from Columbus to Buffalo decrease before this shipping route could become part of the optimal transportation system?
i. Which plant is the most efficiently located plant with respect to transportation costs?
j. What is the meaning of the dual values on demand constraints in LP transporta- tion models?