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Transportation Problems(includes examples) - Linear Programming, Class 12, Math Video Lecture | Mathematics (Maths) Class 12 - JEE
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FAQs on Transportation Problems(includes examples) - Linear Programming, Class 12, Math Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What are transportation problems in the context of linear programming? |  |
Ans. Transportation problems in linear programming refer to optimization problems where the objective is to minimize the cost of transporting goods from a set of sources to a set of destinations, subject to certain constraints.
| 2. Can you provide an example of a transportation problem? | |
Ans. Sure! Let's consider a company that manufactures products at three different factories and needs to transport them to four different warehouses. The transportation costs per unit from each factory to each warehouse are given as follows:
Warehouse 1 Warehouse 2 Warehouse 3 Warehouse 4
Factory 1 $10 $12 $8 $6
Factory 2 $11 $9 $7 $10
Factory 3 $13 $15 $14 $11
The objective is to find the optimal shipment quantities that minimize the total transportation cost while satisfying the supply and demand constraints.
| 3. How are transportation problems solved using linear programming? | |
Ans. Transportation problems can be solved using linear programming techniques, particularly the transportation simplex method. The method involves formulating the problem as a linear program, with decision variables representing the quantities transported from sources to destinations. The objective function is typically the sum of the transportation costs, and the constraints include supply and demand constraints as well as non-negativity constraints for the decision variables. The transportation simplex method iteratively improves the solution until an optimal solution is reached.
| 4. What are the key steps involved in solving a transportation problem through linear programming? | |
Ans. The key steps in solving a transportation problem through linear programming are as follows:
1. Formulate the problem by defining decision variables, objective function, and constraints.
2. Set up the initial feasible solution, often using the North-West Corner Rule or the Least Cost Method.
3. Apply the transportation simplex method to improve the solution iteratively.
4. Check for optimality and stop the iterations once an optimal solution is obtained.
5. Interpret the solution to obtain the optimal shipment quantities and the total transportation cost.
| 5. Are there any real-life applications of transportation problems in various industries? | |
Ans. Yes, transportation problems have various real-life applications in industries such as supply chain management, logistics, and distribution. For example:
- In the manufacturing industry, transportation problems help optimize the allocation of resources and minimize transportation costs for delivering raw materials to factories or finished products to customers.
- In the retail industry, transportation problems assist in determining the most efficient routes for delivering goods to different stores or distribution centers.
- In the healthcare industry, transportation problems aid in optimizing the transportation of medical supplies and equipment between hospitals or clinics.
- In the food industry, transportation problems help to optimize the distribution of perishable goods to different locations, considering factors like shelf life and demand.
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