Distribution Center (S/bushel) Farm 5. Ohio 6. Missouri 7. lowa Supply (bushels) 1. Colorado $- $1.09 1.32 1.22 $1.26 1,600 1,100 1,400 1,900 2. Minnesota 0.89 1.17 3. North Dakota 0.78 1.36 4. Wisconsin 1.19 1.25 1.42 Processing Capacity (bushels) 1,800 2,200 1,600 Plant ($/bushel) Distributlon Center 8. Virginia 9. Pennsylvania 10. Georgia 11. Texas 5. Ohio $4.56 3.43 $3.98 5.74 $4.94 6. Missouri 4.65 5.01 7. Iowa 5.39 6.35 5.70 4.87 Demand (bushels) 1,200 900 1,100 1,500

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The Midlands Field Produce Company contracts with potato farmers in Colorado, Minnesota,
North Dakota, and Wisconsin for monthly potato shipments. Midlands picks up the potatoes at
the farms and ships mostly by truck (and sometimes by rail) to its sorting and distribution centers
in Ohio, Missouri, and Iowa. At these centers the potatoes are cleaned, rejects are discarded, and
the potatoes are sorted according to size and quality. They are then shipped to combination plants
and distribution centers in Virginia, Pennsylvania, Georgia, and Texas, where the company produces
a variety of potato products and distributes bags of potatoes to stores. Exceptions are the
Ohio distribution center, which will accept potatoes only from farms in Minnesota, North Dakota,
and Wisconsin, and the Texas plant, which won’t accept shipments from Ohio because of disagreements
over delivery schedules and quality issues. Following are summaries of the shipping
costs from the farms to the distribution centers and the processing and shipping costs from the
distribution centers to the plants, as well as the available monthly supply at each farm, the processing
capacity at the distribution centers, and the final demand at the plants (in bushels): Formulate and solve a linear programming model to determine the optimal monthly shipments
from the farms to the distribution centers and from the distribution centers to the plants to minimize
total shipping and processing costs. 

Distribution Center (S/bushel)
Farm
5. Ohio
6. Missouri
7. lowa
Supply (bushels)
1. Colorado
$-
$1.09
1.32
1.22
$1.26
1,600
1,100
1,400
1,900
2. Minnesota
0.89
1.17
3. North Dakota
0.78
1.36
4. Wisconsin
1.19
1.25
1.42
Processing Capacity (bushels)
1,800
2,200
1,600
Plant ($/bushel)
Distributlon Center
8. Virginia
9. Pennsylvania
10. Georgia
11. Texas
5. Ohio
$4.56
3.43
$3.98
5.74
$4.94
6. Missouri
4.65
5.01
7. Iowa
5.39
6.35
5.70
4.87
Demand (bushels)
1,200
900
1,100
1,500
Transcribed Image Text:Distribution Center (S/bushel) Farm 5. Ohio 6. Missouri 7. lowa Supply (bushels) 1. Colorado $- $1.09 1.32 1.22 $1.26 1,600 1,100 1,400 1,900 2. Minnesota 0.89 1.17 3. North Dakota 0.78 1.36 4. Wisconsin 1.19 1.25 1.42 Processing Capacity (bushels) 1,800 2,200 1,600 Plant ($/bushel) Distributlon Center 8. Virginia 9. Pennsylvania 10. Georgia 11. Texas 5. Ohio $4.56 3.43 $3.98 5.74 $4.94 6. Missouri 4.65 5.01 7. Iowa 5.39 6.35 5.70 4.87 Demand (bushels) 1,200 900 1,100 1,500
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