Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-28 00:17:15

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: President[i], Vice_President[i], Secretary[i], Treasurer[i], Class_President[i], Class_Senator[i] are binary variables indicating if student i is elected to the respective position
- Operational parameters align with expected linear objective: maximize total_votes = sum(President_Vote[i] * President[i] + Vice_President_Vote[i] * Vice_President[i] + Secretary_Vote[i] * Secretary[i] + Treasurer_Vote[i] * Treasurer[i] + Class_President_Vote[i] * Class_President[i] + Class_Senator_Vote[i] * Class_Senator[i])
- Business logic formulas to express in natural language: Ensures exactly one student is elected to each position (calculation method for Constraint in optimization model), Ensures each student can hold only one position (calculation method for Constraint in optimization model)
- 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": "voter_2",
  "iteration": 1,
  "business_context": "A university is optimizing the allocation of student representatives to various positions based on voting records to maximize student satisfaction, ensuring each position is filled and each student holds only one position.",
  "optimization_problem_description": "Maximize the total number of votes received by elected student representatives across different positions while ensuring that each position is filled by exactly one student and each student can hold at most one position.",
  "optimization_formulation": {
    "objective": "maximize total_votes = sum(President_Vote[i] * President[i] + Vice_President_Vote[i] * Vice_President[i] + Secretary_Vote[i] * Secretary[i] + Treasurer_Vote[i] * Treasurer[i] + Class_President_Vote[i] * Class_President[i] + Class_Senator_Vote[i] * Class_Senator[i])",
    "decision_variables": "President[i], Vice_President[i], Secretary[i], Treasurer[i], Class_President[i], Class_Senator[i] are binary variables indicating if student i is elected to the respective position",
    "constraints": "sum(President[i] for all i) = 1, sum(Vice_President[i] for all i) = 1, sum(Secretary[i] for all i) = 1, sum(Treasurer[i] for all i) = 1, sum(Class_President[i] for all i) = 1, sum(Class_Senator[i] for all i) = 1, President[i] + Vice_President[i] + Secretary[i] + Treasurer[i] + Class_President[i] + Class_Senator[i] <= 1 for all i"
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "President_Vote[i]": {
        "currently_mapped_to": "Voting_record.President_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for President position"
      },
      "Vice_President_Vote[i]": {
        "currently_mapped_to": "Voting_record.Vice_President_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Vice President position"
      },
      "Secretary_Vote[i]": {
        "currently_mapped_to": "Voting_record.Secretary_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Secretary position"
      },
      "Treasurer_Vote[i]": {
        "currently_mapped_to": "Voting_record.Treasurer_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Treasurer position"
      },
      "Class_President_Vote[i]": {
        "currently_mapped_to": "Voting_record.Class_President_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Class President position"
      },
      "Class_Senator_Vote[i]": {
        "currently_mapped_to": "Voting_record.Class_Senator_Vote",
        "mapping_adequacy": "good",
        "description": "Number of votes received by student for Class Senator position"
      }
    },
    "constraint_bounds": {
      "Position_Filled": {
        "currently_mapped_to": "business_configuration_logic.position_filled_constraint",
        "mapping_adequacy": "good",
        "description": "Ensures exactly one student is elected to each position"
      },
      "Student_Position_Limit": {
        "currently_mapped_to": "business_configuration_logic.student_position_limit_constraint",
        "mapping_adequacy": "good",
        "description": "Ensures each student can hold only one position"
      }
    },
    "decision_variables": {
      "President[i]": {
        "currently_mapped_to": "Decision_Variables.President",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as President",
        "variable_type": "binary"
      },
      "Vice_President[i]": {
        "currently_mapped_to": "Decision_Variables.Vice_President",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Vice President",
        "variable_type": "binary"
      },
      "Secretary[i]": {
        "currently_mapped_to": "Decision_Variables.Secretary",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Secretary",
        "variable_type": "binary"
      },
      "Treasurer[i]": {
        "currently_mapped_to": "Decision_Variables.Treasurer",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Treasurer",
        "variable_type": "binary"
      },
      "Class_President[i]": {
        "currently_mapped_to": "Decision_Variables.Class_President",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Class President",
        "variable_type": "binary"
      },
      "Class_Senator[i]": {
        "currently_mapped_to": "Decision_Variables.Class_Senator",
        "mapping_adequacy": "good",
        "description": "Indicates if student is elected as Class Senator",
        "variable_type": "binary"
      }
    }
  },
  "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 tables for decision variables and constraint bounds, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Voting_record (
  President_Vote INTEGER,
  Vice_President_Vote INTEGER,
  Secretary_Vote INTEGER,
  Treasurer_Vote INTEGER,
  Class_President_Vote INTEGER,
  Class_Senator_Vote INTEGER
);

CREATE TABLE Decision_Variables (
  President BOOLEAN,
  Vice_President BOOLEAN,
  Secretary BOOLEAN,
  Treasurer BOOLEAN,
  Class_President BOOLEAN,
  Class_Senator BOOLEAN
);

CREATE TABLE Constraint_Bounds (
  Position_Filled STRING,
  Student_Position_Limit STRING
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical voting scenarios in a university setting, ensuring a diverse distribution of votes across different positions to reflect realistic election outcomes.

-- Realistic data for Voting_record
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (25, 18, 22, 15, 30, 20);
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (30, 25, 20, 18, 28, 22);
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (20, 30, 25, 22, 18, 25);

-- Realistic data for Decision_Variables
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (True, False, False, False, False, False);
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (False, True, False, False, False, False);
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (False, False, True, False, False, False);

-- Realistic data for Constraint_Bounds
INSERT INTO Constraint_Bounds (Position_Filled, Student_Position_Limit) VALUES ('sum(x[i] for all i) = 1', 'x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1');


```

DATA DICTIONARY:
{
  "tables": {
    "Voting_record": {
      "business_purpose": "Stores the number of votes each student received for each position",
      "optimization_role": "objective_coefficients",
      "columns": {
        "President_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for President position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "10, 20, 30"
        },
        "Vice_President_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Vice President position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "5, 15, 25"
        },
        "Secretary_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Secretary position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "8, 18, 28"
        },
        "Treasurer_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Treasurer position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "12, 22, 32"
        },
        "Class_President_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Class President position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "7, 17, 27"
        },
        "Class_Senator_Vote": {
          "data_type": "INTEGER",
          "business_meaning": "Number of votes received by student for Class Senator position",
          "optimization_purpose": "Coefficient in objective function",
          "sample_values": "9, 19, 29"
        }
      }
    },
    "Decision_Variables": {
      "business_purpose": "Stores binary decision variables indicating if a student is elected to a specific position",
      "optimization_role": "decision_variables",
      "columns": {
        "President": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as President",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Vice_President": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Vice President",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Secretary": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Secretary",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Treasurer": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Treasurer",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Class_President": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Class President",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        },
        "Class_Senator": {
          "data_type": "BOOLEAN",
          "business_meaning": "Indicates if student is elected as Class Senator",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "true, false"
        }
      }
    },
    "Constraint_Bounds": {
      "business_purpose": "Stores constraints ensuring each position is filled by exactly one student and each student holds at most one position",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Position_Filled": {
          "data_type": "STRING",
          "business_meaning": "Constraint ensuring each position is filled by exactly one student",
          "optimization_purpose": "Constraint in optimization model",
          "sample_values": "sum(x[i] for all i) = 1"
        },
        "Student_Position_Limit": {
          "data_type": "STRING",
          "business_meaning": "Constraint ensuring each student holds at most one position",
          "optimization_purpose": "Constraint in optimization model",
          "sample_values": "x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "position_filled_constraint": {
    "data_type": "STRING",
    "business_meaning": "Ensures exactly one student is elected to each position",
    "optimization_role": "Constraint in optimization model",
    "configuration_type": "business_logic_formula",
    "formula_expression": "sum(x[i] for all i) = 1"
  },
  "student_position_limit_constraint": {
    "data_type": "STRING",
    "business_meaning": "Ensures each student can hold only one position",
    "optimization_role": "Constraint in optimization model",
    "configuration_type": "business_logic_formula",
    "formula_expression": "x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1 for all i"
  }
}

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: voter_2

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: President[i], Vice_President[i], Secretary[i], Treasurer[i], Class_President[i], Class_Senator[i] are binary variables indicating if student i is elected to the respective position
- Operational parameters align with expected linear objective: maximize total_votes = sum(President_Vote[i] * President[i] + Vice_President_Vote[i] * Vice_President[i] + Secretary_Vote[i] * Secretary[i] + Treasurer_Vote[i] * Treasurer[i] + Class_President_Vote[i] * Class_President[i] + Class_Senator_Vote[i] * Class_Senator[i])
- Business logic formulas to express in natural language: Ensures exactly one student is elected to each position (calculation method for Constraint in optimization model), Ensures each student can hold only one position (calculation method for Constraint in optimization model)
- 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 total_votes = sum(President_Vote[i] * President[i] + Vice_President_Vote[i] * Vice_President[i] + Secretary_Vote[i] * Secretary[i] + Treasurer_Vote[i] * Treasurer[i] + Class_President_Vote[i] * Class_President[i] + Class_Senator_Vote[i] * Class_Senator[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: sum(President[i] for all i) = 1, sum(Vice_President[i] for all i) = 1, sum(Secretary[i] for all i) = 1, sum(Treasurer[i] for all i) = 1, sum(Class_President[i] for all i) = 1, sum(Class_Senator[i] for all i) = 1, President[i] + Vice_President[i] + Secretary[i] + Treasurer[i] + Class_President[i] + Class_Senator[i] <= 1 for all i (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 tables for decision variables and constraint bounds, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Voting_record (
  President_Vote INTEGER,
  Vice_President_Vote INTEGER,
  Secretary_Vote INTEGER,
  Treasurer_Vote INTEGER,
  Class_President_Vote INTEGER,
  Class_Senator_Vote INTEGER
);

CREATE TABLE Decision_Variables (
  President BOOLEAN,
  Vice_President BOOLEAN,
  Secretary BOOLEAN,
  Treasurer BOOLEAN,
  Class_President BOOLEAN,
  Class_Senator BOOLEAN
);

CREATE TABLE Constraint_Bounds (
  Position_Filled STRING,
  Student_Position_Limit STRING
);


```

### 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 typical voting scenarios in a university setting, ensuring a diverse distribution of votes across different positions to reflect realistic election outcomes.

-- Realistic data for Voting_record
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (25, 18, 22, 15, 30, 20);
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (30, 25, 20, 18, 28, 22);
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (20, 30, 25, 22, 18, 25);

-- Realistic data for Decision_Variables
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (True, False, False, False, False, False);
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (False, True, False, False, False, False);
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (False, False, True, False, False, False);

-- Realistic data for Constraint_Bounds
INSERT INTO Constraint_Bounds (Position_Filled, Student_Position_Limit) VALUES ('sum(x[i] for all i) = 1', 'x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1');


```

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

Response:
# Complete Optimization Problem and Solution: voter_2

## 1. Problem Context and Goals

### Context  
The university is focused on optimizing the election of student representatives to various leadership positions. The aim is to maximize student satisfaction by ensuring that the most popular candidates, as determined by voting records, are elected. The decision-making process involves selecting students for the roles of President, Vice President, Secretary, Treasurer, Class President, and Class Senator. Each of these roles is represented by a binary decision variable, indicating whether a student is elected to that position. The operational goal is to maximize the total number of votes received by the elected representatives. This is achieved by summing the votes for each position, weighted by whether the student is elected. The business logic ensures that exactly one student is elected to each position and that no student holds more than one position. This approach aligns with linear optimization principles, focusing on clear, linear relationships without involving complex mathematical operations like products or divisions. The constraints are designed to ensure that each position is filled by exactly one student and that each student can hold only one position, reflecting the university's commitment to fair and efficient representation.

### Goals  
The primary goal of this optimization problem is to maximize the total number of votes received by the elected student representatives. This involves selecting candidates who have received the highest number of votes for each position, thereby ensuring that the elected representatives reflect the preferences of the student body. The success of this optimization is measured by the total votes accumulated across all positions, with the objective being to maximize this total. The linear nature of this goal is emphasized by the straightforward summation of votes, weighted by the binary decision variables indicating election outcomes.

## 2. Constraints    

The constraints for this optimization problem are designed to ensure a fair and efficient election process. Each position must be filled by exactly one student, which means that the sum of the binary decision variables for each position must equal one. Additionally, each student can hold only one position, ensuring that the sum of the decision variables for all positions for a single student does not exceed one. These constraints are expressed in a linear form, aligning with the principles of linear optimization and ensuring that the election process is both fair and efficient.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE Voting_record (
  President_Vote INTEGER,
  Vice_President_Vote INTEGER,
  Secretary_Vote INTEGER,
  Treasurer_Vote INTEGER,
  Class_President_Vote INTEGER,
  Class_Senator_Vote INTEGER
);

CREATE TABLE Decision_Variables (
  President BOOLEAN,
  Vice_President BOOLEAN,
  Secretary BOOLEAN,
  Treasurer BOOLEAN,
  Class_President BOOLEAN,
  Class_Senator BOOLEAN
);

CREATE TABLE Constraint_Bounds (
  Position_Filled STRING,
  Student_Position_Limit STRING
);
```

### Data Dictionary  
The data dictionary provides a comprehensive overview of the tables and columns used in this optimization problem, mapping them to their business purposes and optimization roles. 

- **Voting_record**: This table stores the number of votes each student received for each position. It plays a crucial role in the optimization process by providing the coefficients for the objective function. Each column represents a different position, with the values indicating the number of votes received by a student.

- **Decision_Variables**: This table contains binary decision variables that indicate whether a student is elected to a specific position. Each column corresponds to a different position, and the values are either true or false, representing the election outcome.

- **Constraint_Bounds**: This table stores the constraints that ensure each position is filled by exactly one student and that each student holds at most one position. The constraints are expressed in a linear form, aligning with the optimization model's requirements.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical voting scenarios in a university setting, ensuring a diverse distribution of votes across different positions to reflect realistic election outcomes.

-- Realistic data for Voting_record
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (25, 18, 22, 15, 30, 20);
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (30, 25, 20, 18, 28, 22);
INSERT INTO Voting_record (President_Vote, Vice_President_Vote, Secretary_Vote, Treasurer_Vote, Class_President_Vote, Class_Senator_Vote) VALUES (20, 30, 25, 22, 18, 25);

-- Realistic data for Decision_Variables
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (True, False, False, False, False, False);
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (False, True, False, False, False, False);
INSERT INTO Decision_Variables (President, Vice_President, Secretary, Treasurer, Class_President, Class_Senator) VALUES (False, False, True, False, False, False);

-- Realistic data for Constraint_Bounds
INSERT INTO Constraint_Bounds (Position_Filled, Student_Position_Limit) VALUES ('sum(x[i] for all i) = 1', 'x[i] + y[i] + z[i] + w[i] + u[i] + v[i] <= 1');
```
