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This is a transportation problem where a company has 3 factories and 2 stores. The goal is to find the correct shipment distribution based on the supply from each factory and demand at each store, while minimizing transportation costs.

### Data provided:
- **Production capacity**:
  - Factory 1: 280 units
  - Factory 2: 400 units
  - Factory 3: 350 units
- **Demand**:
  - Store 1: 500 units
  - Store 2: 300 units
- **Cost of transportation (per unit)**:
  - From Factory 1 to Store 1: 15
  - From Factory 1 to Store 2: 25
  - From Factory 2 to Store 1: 10
  - From Factory 2 to Store 2: 50
  - From Factory 3 to Store 1: 8
  - From Factory 3 to Store 2: 34

The restriction in relation to the demand at **Store 1** would be the sum of all units shipped from the factories to Store 1, which must meet the demand of 500 units.

Let:
- \( x_{11} \) = units sent from Factory 1 to Store 1
- \( x_{21} \) = units sent from Factory 2 to Store 1
- \( x_{31} \) = units sent from Factory 3 to Store 1

The equation for the restriction on demand in Store 1 is:

\[
x_{11} + x_{21} + x_{31} = 500
\]

The correct answer is \( x_{11} + x_{21} + x_{31} = 500 \), which matches the second option in your image.

### Questions you might explore:
1. What is the total cost of transportation if the optimal shipment is found?
2. How would increasing demand in Store 2 affect the solution?
3. Can the factories meet a higher demand if production limits are increased by 10%?
4. What is the shadow price of a factory's production limit in this scenario?
5. How would the transportation cost matrix affect the overall solution if transportation costs increased by 5%?

**Tip**: Understanding how constraints like production limits and demand affect transportation problems is crucial in optimizing supply chain logistics.

A company has 3 factories and 2 stores. Each factory has a weekly production capacity, and each store has a weekly demand for product A. The transportation costs per unit from each factory to each store are provided. What is the restriction in relation to the demand at Store 1?

Solve a transportation problem involving three factories and two stores, optimizing shipment costs and balancing production with demand. This problem covers key concepts of linear programming and optimization, including supply-demand constraints and cost minimization.

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