	P	Q	R	S	T	Supply
A	10	2	16	14	10	300
B	6	18	12	13	16	500
C	8	4	14	12	10	825
D	14	22	20	8	18	375
Demand	350	400	250	400	400	

You are likely dealing with a transportation problem, which involves optimizing the cost of distributing a product from several suppliers (A, B, C, D) to several demand points (P, Q, R, S, T). The given table contains the transportation costs between the supply points (A, B, C, D) and demand points (P, Q, R, S, T), as well as the total supply and demand.

Here’s a summary of the given dataYou are likely dealing with a transportation problem, which involves optimizing the cost of distributing a product from several suppliers (A, B, C, D) to several demand points (P, Q, R, S, T). The given table contains the transportation costs between the supply points (A, B, C, D) and demand points (P, Q, R, S, T), as well as the total supply and demand.

Here’s a summary of the given 

|      | P  | Q  | R  | S  | T  | Supply |
|------|----|----|----|----|----|--------|
| A    | 10 | 2  | 16 | 14 | 10 | 300    |
| B    | 6  | 18 | 12 | 13 | 16 | 500    |
| C    | 8  | 4  | 14 | 12 | 10 | 825    |
| D    | 14 | 22 | 20 | 8  | 18 | 375    |
| Demand | 350 | 400 | 250 | 400 | 400 |        |

### Steps to solve:

1. **Check for balanced supply and demand**:
   - Total Supply = 300 + 500 + 825 + 375 = 2000
   - Total Demand = 350 + 400 + 250 + 400 + 400 = 1800

   The total supply (2000) is greater than the total demand (1800). To balance the problem, an artificial demand of 200 units (dummy column) should be introduced to account for the excess supply.

2. **Choose a solution method**: There are several methods to solve this transportation problem, including:
   - **Northwest Corner Method** (simple starting solution)
   - **Least Cost Method** (greedy solution based on the lowest cost)
   - **Vogel's Approximation Method** (more advanced starting solution)
   - **Optimal solution** can be found using the **MODI Method** or **Stepping Stone Method**.

Would you like to proceed with one of these methods for finding the optimal solution or need more details?

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Here are 5 related questions:
1. Do you want to use the Least Cost Method to find an initial solution?
2. Should we apply Vogel's Approximation Method for a better initial solution?
3. Would you like a step-by-step explanation of the Northwest Corner Method?
4. Do you need a detailed explanation of how to balance the supply and demand?
5. Would you prefer an illustration of the MODI or Stepping Stone method for optimality?

**Tip**: Balancing the supply and demand is critical in transportation problems. Always ensure that both sides match before starting the calculations!

The query submitted by the user: P Q R S T Supply A 10 2 16 14 10 300 B 6 18 12 13 16 500 C 8 4 14 12 10 825 D 14 22 20 8 18 375 Demand 350 400 250 400 400

This problem focuses on optimizing transportation costs across multiple supply points and demand locations using methods like Vogel's Approximation and MODI. Total supply is 2000 units, with a demand of 1800 units. Learn the steps to balance and solve this problem effectively.

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