Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-25 22:33:45

Prompt:
You are a business analyst creating structured optimization problem documentation.

DATA SOURCES EXPLANATION:
- FINAL OR ANALYSIS: Final converged optimization problem from alternating process (iteration 1), contains business context and schema mapping evaluation
- DATABASE SCHEMA: Current database structure after iterative adjustments  
- DATA DICTIONARY: Business meanings and optimization roles of tables and columns
- CURRENT STORED VALUES: Realistic business data generated by triple expert (business + data + optimization)
- BUSINESS CONFIGURATION: Scalar parameters and business logic formulas separated from table data

CRITICAL REQUIREMENTS: 
- Ensure problem description naturally leads to LINEAR or MIXED-INTEGER optimization formulation
- Make business context consistent with the intended decision variables and objectives
- Align constraint descriptions with expected mathematical constraints
- Ensure data descriptions map clearly to expected coefficient sources
- Maintain business authenticity while fixing mathematical consistency issues
- Avoid business scenarios that would naturally require nonlinear relationships (variable products, divisions, etc.)

AUTO-EXTRACTED CONTEXT REQUIREMENTS:
- Business decisions match expected decision variables: {'price_in_dollars[i]': 'continuous', 'price_in_euros[i]': 'continuous', 'price_in_pounds[i]': 'continuous'}
- Operational parameters align with expected linear objective: maximize ∑(price_in_dollars[i] * sales_volume[i] + price_in_euros[i] * sales_volume[i] + price_in_pounds[i] * sales_volume[i])
- Business configuration includes: Exchange rate from dollars to euros (used for Used in currency price difference constraints), Exchange rate from dollars to pounds (used for Used in currency price difference constraints), Exchange rate from euros to pounds (used for Used in currency price difference constraints), Maximum allowed price difference between currencies (used for Used in currency price difference constraints)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate

FINAL OR ANALYSIS:
{
  "database_id": "product_catalog",
  "iteration": 1,
  "business_context": "A company aims to optimize its product pricing strategy across multiple currencies (dollars, euros, pounds) to maximize total revenue while ensuring prices remain within acceptable ranges and preventing arbitrage opportunities through controlled price differences.",
  "optimization_problem_description": "Maximize total revenue by adjusting product prices in dollars, euros, and pounds, subject to minimum and maximum price constraints for each currency and ensuring price differences between currencies remain within a specified range.",
  "optimization_formulation": {
    "objective": "maximize \u2211(price_in_dollars[i] * sales_volume[i] + price_in_euros[i] * sales_volume[i] + price_in_pounds[i] * sales_volume[i])",
    "decision_variables": {
      "price_in_dollars[i]": "continuous",
      "price_in_euros[i]": "continuous",
      "price_in_pounds[i]": "continuous"
    },
    "constraints": [
      "min_price_dollars[i] \u2264 price_in_dollars[i] \u2264 max_price_dollars[i]",
      "min_price_euros[i] \u2264 price_in_euros[i] \u2264 max_price_euros[i]",
      "min_price_pounds[i] \u2264 price_in_pounds[i] \u2264 max_price_pounds[i]",
      "|price_in_dollars[i] * exchange_rate_dollars_to_euros - price_in_euros[i]| \u2264 max_price_difference",
      "|price_in_dollars[i] * exchange_rate_dollars_to_pounds - price_in_pounds[i]| \u2264 max_price_difference",
      "|price_in_euros[i] * exchange_rate_euros_to_pounds - price_in_pounds[i]| \u2264 max_price_difference"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "sales_volume[i]": {
        "currently_mapped_to": "Product_Sales_Volume.sales_volume",
        "mapping_adequacy": "good",
        "description": "Expected sales volume for each product, used as coefficients in the objective function"
      }
    },
    "constraint_bounds": {
      "min_price_dollars[i]": {
        "currently_mapped_to": "Product_Price_Constraints.min_price_dollars",
        "mapping_adequacy": "good",
        "description": "Minimum acceptable price in dollars for each product"
      },
      "max_price_dollars[i]": {
        "currently_mapped_to": "Product_Price_Constraints.max_price_dollars",
        "mapping_adequacy": "good",
        "description": "Maximum acceptable price in dollars for each product"
      },
      "min_price_euros[i]": {
        "currently_mapped_to": "Product_Price_Constraints.min_price_euros",
        "mapping_adequacy": "good",
        "description": "Minimum acceptable price in euros for each product"
      },
      "max_price_euros[i]": {
        "currently_mapped_to": "Product_Price_Constraints.max_price_euros",
        "mapping_adequacy": "good",
        "description": "Maximum acceptable price in euros for each product"
      },
      "min_price_pounds[i]": {
        "currently_mapped_to": "Product_Price_Constraints.min_price_pounds",
        "mapping_adequacy": "good",
        "description": "Minimum acceptable price in pounds for each product"
      },
      "max_price_pounds[i]": {
        "currently_mapped_to": "Product_Price_Constraints.max_price_pounds",
        "mapping_adequacy": "good",
        "description": "Maximum acceptable price in pounds for each product"
      },
      "max_price_difference": {
        "currently_mapped_to": "business_configuration_logic.max_price_difference",
        "mapping_adequacy": "good",
        "description": "Maximum allowed price difference between currencies"
      }
    },
    "decision_variables": {
      "price_in_dollars[i]": {
        "currently_mapped_to": "Catalog_Contents.price_in_dollars",
        "mapping_adequacy": "good",
        "description": "Price of the product in dollars, a decision variable in the optimization",
        "variable_type": "continuous"
      },
      "price_in_euros[i]": {
        "currently_mapped_to": "Catalog_Contents.price_in_euros",
        "mapping_adequacy": "good",
        "description": "Price of the product in euros, a decision variable in the optimization",
        "variable_type": "continuous"
      },
      "price_in_pounds[i]": {
        "currently_mapped_to": "Catalog_Contents.price_in_pounds",
        "mapping_adequacy": "good",
        "description": "Price of the product in pounds, a decision variable in the optimization",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for sales volumes and price constraints, modifying the Catalog_Contents table to include foreign keys, and adding business configuration logic for exchange rates and maximum price differences.

CREATE TABLE Product_Sales_Volume (
  product_id INTEGER,
  sales_volume INTEGER
);

CREATE TABLE Product_Price_Constraints (
  product_id INTEGER,
  min_price_dollars FLOAT,
  max_price_dollars FLOAT,
  min_price_euros FLOAT,
  max_price_euros FLOAT,
  min_price_pounds FLOAT,
  max_price_pounds FLOAT
);

CREATE TABLE Catalog_Contents (
  product_id INTEGER,
  price_in_dollars FLOAT,
  price_in_euros FLOAT,
  price_in_pounds FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic market conditions, historical exchange rates, and typical product pricing strategies. Sales volumes were estimated based on product popularity and market demand. Price constraints were set to reflect competitive pricing while allowing for profitability.

-- Realistic data for Product_Sales_Volume
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (1, 150);
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (2, 200);
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (3, 100);

-- Realistic data for Product_Price_Constraints
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (1, 10.0, 50.0, 9.0, 45.0, 8.0, 40.0);
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (2, 15.0, 55.0, 14.0, 50.0, 13.0, 45.0);
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (3, 20.0, 60.0, 19.0, 55.0, 18.0, 50.0);

-- Realistic data for Catalog_Contents
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (1, 25.0, 23.0, 20.0);
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (2, 30.0, 28.0, 25.0);
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (3, 35.0, 32.0, 30.0);


```

DATA DICTIONARY:
{
  "tables": {
    "Product_Sales_Volume": {
      "business_purpose": "Expected sales volume for each product",
      "optimization_role": "objective_coefficients",
      "columns": {
        "product_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each product",
          "optimization_purpose": "Links to Catalog_Contents",
          "sample_values": "1, 2, 3"
        },
        "sales_volume": {
          "data_type": "INTEGER",
          "business_meaning": "Expected sales volume for the product",
          "optimization_purpose": "Used in the objective function",
          "sample_values": "100, 200, 150"
        }
      }
    },
    "Product_Price_Constraints": {
      "business_purpose": "Minimum and maximum acceptable prices for each product in different currencies",
      "optimization_role": "constraint_bounds",
      "columns": {
        "product_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each product",
          "optimization_purpose": "Links to Catalog_Contents",
          "sample_values": "1, 2, 3"
        },
        "min_price_dollars": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum acceptable price in dollars",
          "optimization_purpose": "Used in price constraints",
          "sample_values": "10.0, 15.0, 20.0"
        },
        "max_price_dollars": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum acceptable price in dollars",
          "optimization_purpose": "Used in price constraints",
          "sample_values": "50.0, 55.0, 60.0"
        },
        "min_price_euros": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum acceptable price in euros",
          "optimization_purpose": "Used in price constraints",
          "sample_values": "9.0, 14.0, 19.0"
        },
        "max_price_euros": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum acceptable price in euros",
          "optimization_purpose": "Used in price constraints",
          "sample_values": "45.0, 50.0, 55.0"
        },
        "min_price_pounds": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum acceptable price in pounds",
          "optimization_purpose": "Used in price constraints",
          "sample_values": "8.0, 13.0, 18.0"
        },
        "max_price_pounds": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum acceptable price in pounds",
          "optimization_purpose": "Used in price constraints",
          "sample_values": "40.0, 45.0, 50.0"
        }
      }
    },
    "Catalog_Contents": {
      "business_purpose": "Product catalog with prices in different currencies",
      "optimization_role": "decision_variables",
      "columns": {
        "product_id": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each product",
          "optimization_purpose": "Links to Product_Sales_Volume and Product_Price_Constraints",
          "sample_values": "1, 2, 3"
        },
        "price_in_dollars": {
          "data_type": "FLOAT",
          "business_meaning": "Price of the product in dollars",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "20.0, 25.0, 30.0"
        },
        "price_in_euros": {
          "data_type": "FLOAT",
          "business_meaning": "Price of the product in euros",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "18.0, 23.0, 28.0"
        },
        "price_in_pounds": {
          "data_type": "FLOAT",
          "business_meaning": "Price of the product in pounds",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "16.0, 21.0, 26.0"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "exchange_rate_dollars_to_euros": {
    "data_type": "FLOAT",
    "business_meaning": "Exchange rate from dollars to euros",
    "optimization_role": "Used in currency price difference constraints",
    "configuration_type": "scalar_parameter",
    "value": 0.92,
    "business_justification": "Reflects a realistic exchange rate based on recent market conditions"
  },
  "exchange_rate_dollars_to_pounds": {
    "data_type": "FLOAT",
    "business_meaning": "Exchange rate from dollars to pounds",
    "optimization_role": "Used in currency price difference constraints",
    "configuration_type": "scalar_parameter",
    "value": 0.79,
    "business_justification": "Reflects a realistic exchange rate based on recent market conditions"
  },
  "exchange_rate_euros_to_pounds": {
    "data_type": "FLOAT",
    "business_meaning": "Exchange rate from euros to pounds",
    "optimization_role": "Used in currency price difference constraints",
    "configuration_type": "scalar_parameter",
    "value": 0.86,
    "business_justification": "Reflects a realistic exchange rate based on recent market conditions"
  },
  "max_price_difference": {
    "data_type": "FLOAT",
    "business_meaning": "Maximum allowed price difference between currencies",
    "optimization_role": "Used in currency price difference constraints",
    "configuration_type": "scalar_parameter",
    "value": 5.0,
    "business_justification": "Ensures price differences between currencies are within a reasonable range to prevent arbitrage"
  }
}

Business Configuration Design: 
Our system separates business logic design from value determination:
- Configuration Logic (business_configuration_logic.json): Templates designed by data engineers with sample_value for scalars and actual formulas for business logic
- Configuration Values (business_configuration.json): Realistic values determined by domain experts for scalar parameters only
- Design Rationale: Ensures business logic consistency while allowing flexible parameter tuning


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: product_catalog

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: {'price_in_dollars[i]': 'continuous', 'price_in_euros[i]': 'continuous', 'price_in_pounds[i]': 'continuous'}
- Operational parameters align with expected linear objective: maximize ∑(price_in_dollars[i] * sales_volume[i] + price_in_euros[i] * sales_volume[i] + price_in_pounds[i] * sales_volume[i])
- Business configuration includes: Exchange rate from dollars to euros (used for Used in currency price difference constraints), Exchange rate from dollars to pounds (used for Used in currency price difference constraints), Exchange rate from euros to pounds (used for Used in currency price difference constraints), Maximum allowed price difference between currencies (used for Used in currency price difference constraints)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate
- CRITICAL: Include ALL business configuration information (scalar parameters AND business logic formulas) in natural business language

### Goals  
[Regenerate goals that clearly lead to LINEAR mathematical objective:]
- Optimization goal: maximize
- Metric to optimize: maximize ∑(price_in_dollars[i] * sales_volume[i] + price_in_euros[i] * sales_volume[i] + price_in_pounds[i] * sales_volume[i])
- Success measurement aligned with expected coefficient sources
- Use natural language to precisely describe linear optimization goal
- NO mathematical formulas, equations, or symbolic notation

## 2. Constraints    

[Regenerate constraints that directly match expected LINEAR mathematical constraints:]
- Expected constraint: ['min_price_dollars[i] ≤ price_in_dollars[i] ≤ max_price_dollars[i]', 'min_price_euros[i] ≤ price_in_euros[i] ≤ max_price_euros[i]', 'min_price_pounds[i] ≤ price_in_pounds[i] ≤ max_price_pounds[i]', '|price_in_dollars[i] * exchange_rate_dollars_to_euros - price_in_euros[i]| ≤ max_price_difference', '|price_in_dollars[i] * exchange_rate_dollars_to_pounds - price_in_pounds[i]| ≤ max_price_difference', '|price_in_euros[i] * exchange_rate_euros_to_pounds - price_in_pounds[i]| ≤ max_price_difference'] (Form: Standard constraint form based on business requirements)

[Each constraint should be described in business terms that naturally lead to LINEAR mathematical forms (no variable products or divisions)]

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for sales volumes and price constraints, modifying the Catalog_Contents table to include foreign keys, and adding business configuration logic for exchange rates and maximum price differences.

CREATE TABLE Product_Sales_Volume (
  product_id INTEGER,
  sales_volume INTEGER
);

CREATE TABLE Product_Price_Constraints (
  product_id INTEGER,
  min_price_dollars FLOAT,
  max_price_dollars FLOAT,
  min_price_euros FLOAT,
  max_price_euros FLOAT,
  min_price_pounds FLOAT,
  max_price_pounds FLOAT
);

CREATE TABLE Catalog_Contents (
  product_id INTEGER,
  price_in_dollars FLOAT,
  price_in_euros FLOAT,
  price_in_pounds FLOAT
);


```

### Data Dictionary  
[Create comprehensive business-oriented data dictionary mapping tables and columns to their business purposes and optimization roles - NOT technical database terms. Base this on the data_dictionary provided but rewrite in business language that clearly connects to the expected linear mathematical formulation]

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic market conditions, historical exchange rates, and typical product pricing strategies. Sales volumes were estimated based on product popularity and market demand. Price constraints were set to reflect competitive pricing while allowing for profitability.

-- Realistic data for Product_Sales_Volume
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (1, 150);
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (2, 200);
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (3, 100);

-- Realistic data for Product_Price_Constraints
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (1, 10.0, 50.0, 9.0, 45.0, 8.0, 40.0);
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (2, 15.0, 55.0, 14.0, 50.0, 13.0, 45.0);
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (3, 20.0, 60.0, 19.0, 55.0, 18.0, 50.0);

-- Realistic data for Catalog_Contents
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (1, 25.0, 23.0, 20.0);
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (2, 30.0, 28.0, 25.0);
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (3, 35.0, 32.0, 30.0);


```

STOP HERE - Do not include section 4 (Mathematical Optimization Formulation).

Response:
# Complete Optimization Problem and Solution: product_catalog

## 1. Problem Context and Goals

### Context  
The company operates in a global market, selling products priced in three major currencies: US dollars, euros, and British pounds. To maximize revenue, the company needs to optimize the pricing of its products in each currency while ensuring prices remain within acceptable ranges and preventing arbitrage opportunities. Arbitrage could arise if price differences between currencies exceed a specified threshold, allowing customers to exploit discrepancies for profit.  

The company has established minimum and maximum price limits for each product in each currency to maintain competitiveness and profitability. Additionally, exchange rates between currencies are factored into the pricing strategy to ensure consistency across markets. The exchange rates currently in use are:  
- **Dollars to Euros**: 0.92  
- **Dollars to Pounds**: 0.79  
- **Euros to Pounds**: 0.86  

The maximum allowed price difference between currencies is set at $5.00 to prevent arbitrage. This ensures that prices in different currencies remain aligned after accounting for exchange rate fluctuations.  

The optimization problem focuses on adjusting product prices in dollars, euros, and pounds to maximize total revenue. Revenue is calculated as the sum of the product of each product's price in a currency and its expected sales volume in that currency. The decision variables are the prices in each currency, which can vary continuously within the defined bounds.  

### Goals  
The primary goal is to maximize total revenue across all products and currencies. Revenue is calculated by multiplying each product's price in dollars, euros, and pounds by its expected sales volume and summing these values across all products. Success is measured by achieving the highest possible revenue while adhering to the following constraints:  
1. Prices must remain within the specified minimum and maximum limits for each currency.  
2. Price differences between currencies, after applying exchange rates, must not exceed the maximum allowed difference of $5.00.  

This optimization ensures that the company's pricing strategy is both profitable and consistent across global markets, avoiding scenarios that could lead to arbitrage or customer dissatisfaction.  

## 2. Constraints  

The optimization problem is subject to the following constraints:  
1. **Price Bounds**:  
   - Each product's price in dollars must be between its minimum and maximum acceptable price in dollars.  
   - Each product's price in euros must be between its minimum and maximum acceptable price in euros.  
   - Each product's price in pounds must be between its minimum and maximum acceptable price in pounds.  

2. **Currency Price Differences**:  
   - The difference between a product's price in dollars converted to euros and its price in euros must not exceed the maximum allowed price difference of $5.00.  
   - The difference between a product's price in dollars converted to pounds and its price in pounds must not exceed the maximum allowed price difference of $5.00.  
   - The difference between a product's price in euros converted to pounds and its price in pounds must not exceed the maximum allowed price difference of $5.00.  

These constraints ensure that prices remain competitive, profitable, and consistent across currencies, preventing arbitrage opportunities.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for sales volumes and price constraints, modifying the Catalog_Contents table to include foreign keys, and adding business configuration logic for exchange rates and maximum price differences.

CREATE TABLE Product_Sales_Volume (
  product_id INTEGER,
  sales_volume INTEGER
);

CREATE TABLE Product_Price_Constraints (
  product_id INTEGER,
  min_price_dollars FLOAT,
  max_price_dollars FLOAT,
  min_price_euros FLOAT,
  max_price_euros FLOAT,
  min_price_pounds FLOAT,
  max_price_pounds FLOAT
);

CREATE TABLE Catalog_Contents (
  product_id INTEGER,
  price_in_dollars FLOAT,
  price_in_euros FLOAT,
  price_in_pounds FLOAT
);
```

### Data Dictionary  
- **Product_Sales_Volume**:  
  - **Purpose**: Stores the expected sales volume for each product.  
  - **Optimization Role**: Provides coefficients for the revenue calculation in the objective function.  
  - **Columns**:  
    - `product_id`: Unique identifier for each product.  
    - `sales_volume`: Expected sales volume for the product.  

- **Product_Price_Constraints**:  
  - **Purpose**: Defines the minimum and maximum acceptable prices for each product in dollars, euros, and pounds.  
  - **Optimization Role**: Provides bounds for the price constraints.  
  - **Columns**:  
    - `product_id`: Unique identifier for each product.  
    - `min_price_dollars`: Minimum acceptable price in dollars.  
    - `max_price_dollars`: Maximum acceptable price in dollars.  
    - `min_price_euros`: Minimum acceptable price in euros.  
    - `max_price_euros`: Maximum acceptable price in euros.  
    - `min_price_pounds`: Minimum acceptable price in pounds.  
    - `max_price_pounds`: Maximum acceptable price in pounds.  

- **Catalog_Contents**:  
  - **Purpose**: Stores the current prices of products in dollars, euros, and pounds.  
  - **Optimization Role**: Contains the decision variables for the optimization problem.  
  - **Columns**:  
    - `product_id`: Unique identifier for each product.  
    - `price_in_dollars`: Price of the product in dollars.  
    - `price_in_euros`: Price of the product in euros.  
    - `price_in_pounds`: Price of the product in pounds.  

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic market conditions, historical exchange rates, and typical product pricing strategies. Sales volumes were estimated based on product popularity and market demand. Price constraints were set to reflect competitive pricing while allowing for profitability.

-- Realistic data for Product_Sales_Volume
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (1, 150);
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (2, 200);
INSERT INTO Product_Sales_Volume (product_id, sales_volume) VALUES (3, 100);

-- Realistic data for Product_Price_Constraints
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (1, 10.0, 50.0, 9.0, 45.0, 8.0, 40.0);
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (2, 15.0, 55.0, 14.0, 50.0, 13.0, 45.0);
INSERT INTO Product_Price_Constraints (product_id, min_price_dollars, max_price_dollars, min_price_euros, max_price_euros, min_price_pounds, max_price_pounds) VALUES (3, 20.0, 60.0, 19.0, 55.0, 18.0, 50.0);

-- Realistic data for Catalog_Contents
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (1, 25.0, 23.0, 20.0);
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (2, 30.0, 28.0, 25.0);
INSERT INTO Catalog_Contents (product_id, price_in_dollars, price_in_euros, price_in_pounds) VALUES (3, 35.0, 32.0, 30.0);
```
