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 either Excel Solver or QM-for-Windows ]. What would be the optimal transportation plan, and the total transportation cost?
Critical Path Method
The critical path is the longest succession of tasks that has to be successfully completed to conclude a project entirely. The tasks involved in the sequence are called critical activities, as any task getting delayed will result in the whole project getting delayed. To determine the time duration of a project, the critical path has to be identified. The critical path method or CPM is used by project managers to evaluate the least amount of time required to finish each task with the least amount of delay.
Cost Analysis
The entire idea of cost of production or definition of production cost is applied corresponding or we can say that it is related to investment or money cost. Money cost or investment refers to any money expenditure which the firm or supplier or producer undertakes in purchasing or hiring factor of production or factor services.
Inventory Management
Inventory management is the process or system of handling all the goods that an organization owns. In simpler terms, inventory management deals with how a company orders, stores, and uses its goods.
Project Management
Project Management is all about management and optimum utilization of the resources in the best possible manner to develop the software as per the requirement of the client. Here the Project refers to the development of software to meet the end objective of the client by providing the required product or service within a specified Period of time and ensuring high quality. This can be done by managing all the available resources. In short, it can be defined as an application of knowledge, skills, tools, and techniques to meet the objective of the Project. It is the duty of a Project Manager to achieve the objective of the Project as per the specifications given by the client.
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 either Excel Solver or QM-for-Windows ]. What would be the optimal transportation plan, and the total transportation cost?
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