What are the constraints A soft drink manufacturing company has three factories—one in Orlando, one in Tampa, and one in Port St. Lucie—that supply soft drink bottles to three warehouses located in the city of Miami. The associated per-unit transportation cost between the factories and the warehouses is provided in the table below.**Transportation Costs ($)**| Factories/Warehouse (W) | W1 | W2 | W3 ||-------------------------|----|----|----|| Orlando | 7 | 4 | 5 || Tampa | 7 | 6 | 4 || Port St. Lucie | 5 | 5 | 6 |- The factory in Orlando has a capacity of 14,000 units.- The factory in Tampa has a capacity of 25,000 units.- The factory in Port St. Lucie has a capacity of 23,000 units.The requirements of the warehouses are:| Warehouse | Requirement (Bottles) ||-----------|-----------------------|| W1 | 18,000 || W2 | 19,000 || W3 | 22,000 |Determine how much of the company’s production should be shipped from each factory to each warehouse in order to minimize the total transportation cost. The image shows a spreadsheet aimed at optimizing a transportation problem involving three factories and three warehouses. Here's a detailed transcription:### Transportation Costs ($)- **Factories/Warehouse (W)** - Costco Warehouses: W1, W2, W3 - **Orlando** - Costs: W1 - $7, W2 - $4, W3 - $5 - **Tampa** - Costs: W1 - $7, W2 - $6, W3 - $4 - **Port St. Lucie** - Costs: W1 - $5, W2 - $5, W3 - $6- **Warehouse Requirement (Bottles)** - W1: 18,000 bottles - W2: 19,000 bottles - W3: 22,000 bottles### Model- **Production to be Shipped** - Factories: Orlando, Tampa, Port St. Lucie - Each factory's shipments are initially set to 0 for W1, W2, and W3.### Capacity- **Orlando** - 14,000 bottles- **Tampa** - 25,000 bottles- **Port St. Lucie** - 23,000 bottles### Constraints- The grid for "Constraints" does not have any specified constraints yet.### Formula for Outcome- The outcome is calculated using the formula: - `C11*B10+C21*C10+C31*D10+C12*B11+C22*D11+C32*D12+C13*B12+C23*C12+C33*D12` This formula likely represents the total transportation cost, calculated by summing the products of shipment quantities and respective costs.### Minimum- The column titled "Minimum" is adjacent but currently without data.This setup is typical for modeling transportation or supply chain problems where the goal is to minimize costs while meeting production and demand constraints.

This is a transportation problem. As from the excel image, let's consider each decision variable as Cij where i = Warehouse number, j = Supply Factory number Objective function is to minimize the costs and is already given as a sum product in cell G9. Given Capacities, Orlando - 14000 Tampa - 25000 Port St. Lucie - 23000 Given requirements, W1 - 18000 W2 - 19000 W3 - 22000Constraints are to limit the number of units transferring from each factory and also meet the requirements for each warehouse. Capacity constraints: Orlando constraint : 7*C11 + 4*C21 + 5*C31 <= 14000 Tampa constraint : 7*C12 + 6*C22 + 4*C32 <= 25000 Port St.Lucie constraint : 5*C13 + 5*C23 + 6*C33 <= 23000 Requirement constraints: W1 constraint : 7*C11 + 7*C12 + 5*C13 = 18000 W2 constraint : 4*C21 + 6*C22 + 5*C23 = 19000 W3 constraint : 5*C31 + 4*C32 + 6*C33 = 22000

Answered: What are the constraints

Business

Operations Management

What are the constraints

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

What are the constraints

A soft drink manufacturing company has three factories—one in Orlando, one in Tampa, and one in Port St. Lucie—that supply soft drink bottles to three warehouses located in the city of Miami. The associated per-unit transportation cost between the factories and the warehouses is provided in the table below.

**Transportation Costs ($)**

| Factories/Warehouse (W) | W1 | W2 | W3 |
|-------------------------|----|----|----|
| Orlando | 7 | 4 | 5 |
| Tampa | 7 | 6 | 4 |
| Port St. Lucie | 5 | 5 | 6 |

- The factory in Orlando has a capacity of 14,000 units.
- The factory in Tampa has a capacity of 25,000 units.
- The factory in Port St. Lucie has a capacity of 23,000 units.

The requirements of the warehouses are:

| Warehouse | Requirement (Bottles) |
|-----------|-----------------------|
| W1 | 18,000 |
| W2 | 19,000 |
| W3 | 22,000 |

Determine how much of the company’s production should be shipped from each factory to each warehouse in order to minimize the total transportation cost.

The image shows a spreadsheet aimed at optimizing a transportation problem involving three factories and three warehouses. Here's a detailed transcription:

### Transportation Costs ($)
- **Factories/Warehouse (W)**
- Costco Warehouses: W1, W2, W3
- **Orlando**
- Costs: W1 - $7, W2 - $4, W3 - $5
- **Tampa**
- Costs: W1 - $7, W2 - $6, W3 - $4
- **Port St. Lucie**
- Costs: W1 - $5, W2 - $5, W3 - $6
- **Warehouse Requirement (Bottles)**
- W1: 18,000 bottles
- W2: 19,000 bottles
- W3: 22,000 bottles

### Model
- **Production to be Shipped**
- Factories: Orlando, Tampa, Port St. Lucie
- Each factory's shipments are initially set to 0 for W1, W2, and W3.

### Capacity
- **Orlando** - 14,000 bottles
- **Tampa** - 25,000 bottles
- **Port St. Lucie** - 23,000 bottles

### Constraints
- The grid for "Constraints" does not have any specified constraints yet.

### Formula for Outcome
- The outcome is calculated using the formula:
- `C11*B10+C21*C10+C31*D10+C12*B11+C22*D11+C32*D12+C13*B12+C23*C12+C33*D12`

This formula likely represents the total transportation cost, calculated by summing the products of shipment quantities and respective costs.

### Minimum
- The column titled "Minimum" is adjacent but currently without data.

This setup is typical for modeling transportation or supply chain problems where the goal is to minimize costs while meeting production and demand constraints.

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