PLEASE ANSWER STEP BY STEP AND ON EXCEL **Contois Carpets Production and Inventory Network Diagram**Contois Carpets is a small manufacturer specializing in carpeting for home and office installations. The diagram below provides a detailed view of the production capacities, demand, and associated costs for the next four quarters. These elements include production capacity, demand, production cost per square yard (in dollars), and inventory holding cost per square yard (in dollars).### Network Diagram Explanation- **Nodes:** - **Beginning Inventory (Node 1):** Starts with an inventory of 50 square yards. - **Production Nodes:** - **Quarter 1 Production (Node 2):** Capacity of 600 square yards. - **Quarter 2 Production (Node 3):** Capacity of 300 square yards. - **Quarter 3 Production (Node 4):** Capacity of 500 square yards. - **Quarter 4 Production (Node 5):** Capacity of 400 square yards. - **Demand Nodes:** - **Quarter 1 Demand (Node 6):** 400 square yards. - **Quarter 2 Demand (Node 7):** 500 square yards. - **Quarter 3 Demand (Node 8):** 400 square yards. - **Quarter 4 Demand (Node 9):** 400 square yards. - **Ending Inventory (Node 10):** A target of 100 square yards.- **Production Costs:** - Cost per square yard for Quarter 1 is 2 dollars. - Cost per square yard for Quarter 2 is 5 dollars. - Cost per square yard for Quarter 3 and Quarter 4 is 3 dollars each.- **Inventory Holding Cost:** - A consistent holding cost of 0.25 dollars per square yard is applied across quarters.- **Arcs Indicate:** - Inventory flow between periods indicating transitions from production to demand nodes and inventory carry overs.This visual representation aids in understanding the flow and balance required to meet demands efficiently while considering costs across multiple quarters. ### Linear Programming Model for Carpet Production#### Objective:Develop a linear programming model to minimize cost.#### Parameters:- Let $ x_{ij} $ be the number of square yards of carpet which flows from node $ i $ to node $ j $.#### Constraints:- **Minimize**: - [Input Box]- **Subject to (s.t.):** - **Beginning Inventory Flow**: - [Input Box] - **Quarter 1 Production Flow**: - [Input Box] - **Quarter 2 Production Flow**: - [Input Box] - **Quarter 3 Production Flow**: - [Input Box] - **Quarter 4 Production Flow**: - [Input Box] - **Quarter 1 Demand Flow**: - [Input Box] - **Quarter 2 Demand Flow**: - [Input Box] - **Quarter 3 Demand Flow**: - [Input Box] - **Quarter 4 Demand Flow**: - [Input Box] - **Ending Inventory Flow**: - [Input Box]- $ x_{ij} \geq 0 $ for all $ i, j $.#### Solution:Solve the linear program to find the optimal solution (in dollars).- $(x_{16}, x_{26}, x_{37}, x_{48}, x_{59}, x_{67}, x_{78}, x_{89}, x_{910}) = ([\text{Input Box}])$ with cost \$[\text{Input Box}].

Linear programming is a mathematical technique that is also used in operations management…

Develop a linear programming model to minimize cost. (Let x, be the number of square yards of carpet which flows from node / to node j.) Min s.t. Beginning Inventory Flow Quarter 1 Production Flow Quarter 2 Production Flow Quarter 3 Production Flow Quarter 4 Production Flow Quarter 1 Demand Flow Quarter 2 Demand Flow Quarter 3 Demand Flow Quarter 4 Demand Flow Ending Inventory Flow x 20 for all i, J. Solve the linear program to find the optimal solution (in dollars). (X16 X26X371 X48 X591 X671 X78X89 X910) - with cost $

Develop a linear programming model to minimize cost. (Let x, be the number of square yards of carpet which flows from node / to node j.) Min s.t. Beginning Inventory Flow Quarter 1 Production Flow Quarter 2 Production Flow Quarter 3 Production Flow Quarter 4 Production Flow Quarter 1 Demand Flow Quarter 2 Demand Flow Quarter 3 Demand Flow Quarter 4 Demand Flow Ending Inventory Flow x 20 for all i, J. Solve the linear program to find the optimal solution (in dollars). (X16 X26X371 X48 X591 X671 X78X89 X910) - with cost $

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

PLEASE ANSWER STEP BY STEP AND ON EXCEL

**Contois Carpets Production and Inventory Network Diagram**

Contois Carpets is a small manufacturer specializing in carpeting for home and office installations. The diagram below provides a detailed view of the production capacities, demand, and associated costs for the next four quarters. These elements include production capacity, demand, production cost per square yard (in dollars), and inventory holding cost per square yard (in dollars).

### Network Diagram Explanation

- **Nodes:**
- **Beginning Inventory (Node 1):** Starts with an inventory of 50 square yards.
- **Production Nodes:**
- **Quarter 1 Production (Node 2):** Capacity of 600 square yards.
- **Quarter 2 Production (Node 3):** Capacity of 300 square yards.
- **Quarter 3 Production (Node 4):** Capacity of 500 square yards.
- **Quarter 4 Production (Node 5):** Capacity of 400 square yards.
- **Demand Nodes:**
- **Quarter 1 Demand (Node 6):** 400 square yards.
- **Quarter 2 Demand (Node 7):** 500 square yards.
- **Quarter 3 Demand (Node 8):** 400 square yards.
- **Quarter 4 Demand (Node 9):** 400 square yards.
- **Ending Inventory (Node 10):** A target of 100 square yards.

- **Production Costs:**
- Cost per square yard for Quarter 1 is 2 dollars.
- Cost per square yard for Quarter 2 is 5 dollars.
- Cost per square yard for Quarter 3 and Quarter 4 is 3 dollars each.

- **Inventory Holding Cost:**
- A consistent holding cost of 0.25 dollars per square yard is applied across quarters.

- **Arcs Indicate:**
- Inventory flow between periods indicating transitions from production to demand nodes and inventory carry overs.

This visual representation aids in understanding the flow and balance required to meet demands efficiently while considering costs across multiple quarters.

### Linear Programming Model for Carpet Production

#### Objective:
Develop a linear programming model to minimize cost.

#### Parameters:
- Let $ x_{ij} $ be the number of square yards of carpet which flows from node $ i $ to node $ j $.

#### Constraints:
- **Minimize**:
- [Input Box]

- **Subject to (s.t.):**
- **Beginning Inventory Flow**:
- [Input Box]
- **Quarter 1 Production Flow**:
- [Input Box]
- **Quarter 2 Production Flow**:
- [Input Box]
- **Quarter 3 Production Flow**:
- [Input Box]
- **Quarter 4 Production Flow**:
- [Input Box]
- **Quarter 1 Demand Flow**:
- [Input Box]
- **Quarter 2 Demand Flow**:
- [Input Box]
- **Quarter 3 Demand Flow**:
- [Input Box]
- **Quarter 4 Demand Flow**:
- [Input Box]
- **Ending Inventory Flow**:
- [Input Box]

- $ x_{ij} \geq 0 $ for all $ i, j $.

#### Solution:
Solve the linear program to find the optimal solution (in dollars).

- $(x_{16}, x_{26}, x_{37}, x_{48}, x_{59}, x_{67}, x_{78}, x_{89}, x_{910}) = ([\text{Input Box}])$ with cost \$[\text{Input Box}].

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