Green Valley Mills produces carpet at plants in (1)St. Louis, (2)Richmond, and (3)Nashville. The carpet is then shipped to four outlets, located in (1)Chicago, (2)Atlanta, (3)Dallas, and (4)Pittsburgh. The cost per ton of shipping carpet from each of the three plants to the four outlets, plant capacity, and demand required at each outlet are as follows: From/To 1 2 3 4 Supply Available St. Louis $500 $750 $300 $450 20 tons Richmond $650 $800 $400 $600 17 tons Nashville $400 $700 $500 $550 18 tons Demand Required 10 tons 11 tons 13 tons 14 tons Please formulate a linear programming model by defining the decision variables, objective function, and constraints, which will be used to help Green Valley determine the best amount of carpet shipped from each plant to each outlet in order to minimize the total transportation cost. What is the total transportation cost for the problem? You can address this Linear Programming problem in the following separate steps. Q1. Please clearly define all decision variables. Q2. Using the variables defined, please give the objective function. Q3. Please give the constraints for the problem. Q4. Please solve this linear programming problem using Excel solver or QM-for-Windows What would be the optimal transportation plan, and the total transportation cost?
Green Valley Mills produces carpet at plants in (1)St. Louis, (2)Richmond, and (3)Nashville. The carpet is then shipped to four outlets, located in (1)Chicago, (2)Atlanta, (3)Dallas, and (4)Pittsburgh. The cost per ton of shipping carpet from each of the three plants to the four outlets, plant capacity, and demand required at each outlet are as follows:
| From/To | 1 | 2 | 3 | 4 | Supply Available |
| St. Louis | $500 | $750 | $300 | $450 | 20 tons |
| Richmond | $650 | $800 | $400 | $600 | 17 tons |
| Nashville | $400 | $700 | $500 | $550 | 18 tons |
| Demand Required | 10 tons | 11 tons | 13 tons | 14 tons |
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Please formulate a linear programming model by defining the decision variables, objective function, and constraints, which will be used to help Green Valley determine the best amount of carpet shipped from each plant to each outlet in order to minimize the total transportation cost.
What is the total transportation cost for the problem? You can address this Linear Programming problem in the following separate steps.
Q1. Please clearly define all decision variables.
Q2. Using the variables defined, please give the objective function.
Q3. Please give the constraints for the problem.
Q4. Please solve this linear programming problem using Excel solver or QM-for-Windows What would be the optimal transportation plan, and the total transportation cost?
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