Situation A DescriptionA global supplier of denim jeans for apparel companies purchases raw cotton from producers in Arkansas, Mississippi, and Texas. The bales (550 lbs. per) are transported to ports in Houston, New Orleans, Savannah, and Charleston for shipment to denim fabric factories in Shanghai, Karachi, and Saigon. The denim (a bale of cotton produces approximately 325 yards of denim fabric) is then shipped to facilities in China, India, Japan, Turkey, and Italy for final production of denim jeans.Tables with shipping costs, supply, and demand for two stages of the production process as presented in the following tables. Ports Cotton Farms 4. Houston 5. Savannah 6. New Orleans 7. Charleston Supply (bales) 1. Arkansas $18 $23 $15 $23 31,000 2. Mississippi 26 19 14 27 45,000 3. Texas 14 29 21 32 27,000Demand (bales) 26,000 19,000 14,000 12,000 Denim Fabric PlantsPorts 8. Shanghai 9. Karachi 10. Saigon 4. Houston $23 $28 $30 5. Savannah 28 24 32 6. New Orleans 26 26 27 7. Charleston 29 23 34Demand (bales) 34,000 22,000 15,000 In the linear programming model formulation for this problem Xi_j = the number of bales shipped from the farms (i = 1,2,3) to the distribution centers (j = 4,5,6,7), and from the distribution centers (i = 4,5,6,7) to the denim fabric plants (j = 8,9,10). Please answer the following question(s). Flag question: Question 2Question 2Tips10.25 ptsFor situation A (above) what is the transshipment constraint for the warehouse in Charleston (𝑥7)?
Question
Situation A DescriptionA global supplier of denim jeans for apparel companies purchases raw cotton from producers in Arkansas, Mississippi, and Texas. The bales (550 lbs. per) are transported to ports in Houston, New Orleans, Savannah, and Charleston for shipment to denim fabric factories in Shanghai, Karachi, and Saigon. The denim (a bale of cotton produces approximately 325 yards of denim fabric) is then shipped to facilities in China, India, Japan, Turkey, and Italy for final production of denim jeans.Tables with shipping costs, supply, and demand for two stages of the production process as presented in the following tables. Ports Cotton Farms 4. Houston 5. Savannah 6. New Orleans 7. Charleston Supply (bales) 1. Arkansas 23 23 31,000 2. Mississippi 26 19 14 27 45,000 3. Texas 14 29 21 32 27,000Demand (bales) 26,000 19,000 14,000 12,000 Denim Fabric PlantsPorts 8. Shanghai 9. Karachi 10. Saigon 4. Houston 28 $30 5. Savannah 28 24 32 6. New Orleans 26 26 27 7. Charleston 29 23 34Demand (bales) 34,000 22,000 15,000 In the linear programming model formulation for this problem Xi_j = the number of bales shipped from the farms (i = 1,2,3) to the distribution centers (j = 4,5,6,7), and from the distribution centers (i = 4,5,6,7) to the denim fabric plants (j = 8,9,10). Please answer the following question(s). Flag question: Question 2Question 2Tips10.25 ptsFor situation A (above) what is the transshipment constraint for the warehouse in Charleston (𝑥7)?
Solution
The transshipment constraint for the warehouse in Charleston (x7) is the balance between the supply of cotton bales received from the farms and the demand of cotton bales shipped to the denim fabric plants.
In mathematical terms, it can be represented as:
x1_7 + x2_7 + x3_7 = x7_8 + x7_9 + x7_10
Where:
- x1_7, x2_7, x3_7 are the number of bales shipped from the farms in Arkansas, Mississippi, and Texas to Charleston respectively.
- x7_8, x7_9, x7_10 are the number of bales shipped from Charleston to the denim fabric plants in Shanghai, Karachi, and Saigon respectively.
This equation ensures that the number of bales received by Charleston from the farms equals the number of bales it ships to the denim fabric plants, thus maintaining the balance of supply and demand.
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