Iteration final - PROBLEM_DESCRIPTION
Sequence: 9
Timestamp: 2025-07-25 22:42:04

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 3), 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: Scholarship_Amount[i] (continuous)
- Operational parameters align with expected linear objective: maximize ∑(w1 * GPA[i] + w2 * HoursPerWeek[i] + w3 * Hours_Played[i])
- Business configuration includes: Total budget available for scholarships (used for Constraint bound in optimization model), Factor to ensure higher GPA students receive more scholarships (used for Constraint bound 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": "game_1",
  "iteration": 3,
  "business_context": "A university aims to optimize scholarship allocation to students based on academic performance, sports participation, and gaming habits to maximize overall student satisfaction and performance while adhering to budget and participation constraints.",
  "optimization_problem_description": "Maximize the total weighted sum of student satisfaction, which is influenced by academic performance, sports participation, and gaming habits, subject to budget limits, minimum and maximum hours for sports and gaming, and ensuring students with higher academic performance receive more scholarships.",
  "optimization_formulation": {
    "objective": "maximize \u2211(w1 * GPA[i] + w2 * HoursPerWeek[i] + w3 * Hours_Played[i])",
    "decision_variables": "Scholarship_Amount[i] (continuous)",
    "constraints": [
      "\u2211(Scholarship_Amount[i]) \u2264 Total_Budget",
      "Scholarship_Amount[i] \u2265 Scholarship_Factor * GPA[i]",
      "Min_Hours_Sports[i] \u2264 HoursPerWeek[i] \u2264 Max_Hours_Sports[i]",
      "Min_Hours_Gaming[i] \u2264 Hours_Played[i] \u2264 Max_Hours_Gaming[i]"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "w1": {
        "currently_mapped_to": "Objective_Weights.w1",
        "mapping_adequacy": "good",
        "description": "Weight for academic performance"
      },
      "w2": {
        "currently_mapped_to": "Objective_Weights.w2",
        "mapping_adequacy": "good",
        "description": "Weight for sports participation"
      },
      "w3": {
        "currently_mapped_to": "Objective_Weights.w3",
        "mapping_adequacy": "good",
        "description": "Weight for gaming habits"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for scholarships"
      },
      "Scholarship_Factor": {
        "currently_mapped_to": "business_configuration_logic.Scholarship_Factor",
        "mapping_adequacy": "good",
        "description": "Factor to ensure higher GPA students receive more scholarships"
      },
      "Min_Hours_Sports[i]": {
        "currently_mapped_to": "SportsInfo.Min_Hours_Sports",
        "mapping_adequacy": "good",
        "description": "Minimum hours required for sports participation"
      },
      "Max_Hours_Sports[i]": {
        "currently_mapped_to": "SportsInfo.Max_Hours_Sports",
        "mapping_adequacy": "good",
        "description": "Maximum hours allowed for sports participation"
      },
      "Min_Hours_Gaming[i]": {
        "currently_mapped_to": "Plays_Games.Min_Hours_Gaming",
        "mapping_adequacy": "good",
        "description": "Minimum hours required for gaming"
      },
      "Max_Hours_Gaming[i]": {
        "currently_mapped_to": "Plays_Games.Max_Hours_Gaming",
        "mapping_adequacy": "good",
        "description": "Maximum hours allowed for gaming"
      }
    },
    "decision_variables": {
      "Scholarship_Amount[i]": {
        "currently_mapped_to": "Scholarship_Allocation.Scholarship_Amount",
        "mapping_adequacy": "good",
        "description": "Scholarship amount allocated to the student",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 3 Database Schema
-- Objective: Schema changes include adding missing optimization requirements to business configuration logic and ensuring all mappings are complete.

CREATE TABLE Academic_Performance (
  Student_ID INTEGER,
  GPA FLOAT
);

CREATE TABLE Objective_Weights (
  w1 FLOAT,
  w2 FLOAT,
  w3 FLOAT
);

CREATE TABLE SportsInfo (
  Student_ID INTEGER,
  HoursPerWeek FLOAT,
  Min_Hours_Sports FLOAT,
  Max_Hours_Sports FLOAT
);

CREATE TABLE Plays_Games (
  Student_ID INTEGER,
  Hours_Played FLOAT,
  Min_Hours_Gaming FLOAT,
  Max_Hours_Gaming FLOAT
);

CREATE TABLE Scholarship_Allocation (
  Student_ID INTEGER,
  Scholarship_Amount FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic university scholarship allocation scenarios, considering typical GPA ranges, sports and gaming participation hours, and budget constraints.

-- Realistic data for Academic_Performance
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (1, 3.8);
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (2, 3.5);
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (3, 3.2);

-- Realistic data for Objective_Weights
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.6, 0.25, 0.15);
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.5, 0.3, 0.2);
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.4, 0.35, 0.25);

-- Realistic data for SportsInfo
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (1, 10.0, 2.0, 15.0);
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (2, 7.5, 2.5, 18.0);
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (3, 5.0, 3.0, 20.0);

-- Realistic data for Plays_Games
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (1, 12.5, 5.0, 20.0);
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (2, 15.0, 6.0, 25.0);
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (3, 10.0, 5.5, 22.0);

-- Realistic data for Scholarship_Allocation
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (1, 3000.0);
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (2, 2000.0);
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (3, 1000.0);


```

DATA DICTIONARY:
{
  "tables": {
    "Academic_Performance": {
      "business_purpose": "Academic performance metrics for students",
      "optimization_role": "business_data",
      "columns": {
        "Student_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Links academic performance to student",
          "sample_values": "1, 2, 3"
        },
        "GPA": {
          "data_type": "FLOAT",
          "business_meaning": "Grade Point Average of the student",
          "optimization_purpose": "Used in objective function and constraints",
          "sample_values": "3.5, 4.0, 3.7"
        }
      }
    },
    "Objective_Weights": {
      "business_purpose": "Weights for objective function components",
      "optimization_role": "objective_coefficients",
      "columns": {
        "w1": {
          "data_type": "FLOAT",
          "business_meaning": "Weight for academic performance",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.5, 0.6, 0.4"
        },
        "w2": {
          "data_type": "FLOAT",
          "business_meaning": "Weight for sports participation",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.3, 0.2, 0.25"
        },
        "w3": {
          "data_type": "FLOAT",
          "business_meaning": "Weight for gaming habits",
          "optimization_purpose": "Used in objective function",
          "sample_values": "0.2, 0.15, 0.2"
        }
      }
    },
    "SportsInfo": {
      "business_purpose": "Sports participation data for students",
      "optimization_role": "business_data",
      "columns": {
        "Student_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Links sports participation to student",
          "sample_values": "1, 2, 3"
        },
        "HoursPerWeek": {
          "data_type": "FLOAT",
          "business_meaning": "Hours spent on sports per week",
          "optimization_purpose": "Used in objective function and constraints",
          "sample_values": "5.0, 10.0, 7.5"
        },
        "Min_Hours_Sports": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum hours required for sports participation",
          "optimization_purpose": "Constraint bound",
          "sample_values": "2.0, 3.0, 2.5"
        },
        "Max_Hours_Sports": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum hours allowed for sports participation",
          "optimization_purpose": "Constraint bound",
          "sample_values": "15.0, 20.0, 18.0"
        }
      }
    },
    "Plays_Games": {
      "business_purpose": "Gaming habits data for students",
      "optimization_role": "business_data",
      "columns": {
        "Student_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Links gaming habits to student",
          "sample_values": "1, 2, 3"
        },
        "Hours_Played": {
          "data_type": "FLOAT",
          "business_meaning": "Hours spent on gaming per week",
          "optimization_purpose": "Used in objective function and constraints",
          "sample_values": "10.0, 15.0, 12.5"
        },
        "Min_Hours_Gaming": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum hours required for gaming",
          "optimization_purpose": "Constraint bound",
          "sample_values": "5.0, 6.0, 5.5"
        },
        "Max_Hours_Gaming": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum hours allowed for gaming",
          "optimization_purpose": "Constraint bound",
          "sample_values": "20.0, 25.0, 22.0"
        }
      }
    },
    "Scholarship_Allocation": {
      "business_purpose": "Scholarship amounts allocated to each student",
      "optimization_role": "decision_variables",
      "columns": {
        "Student_ID": {
          "data_type": "INTEGER",
          "business_meaning": "Unique identifier for each student",
          "optimization_purpose": "Links scholarship allocation to student",
          "sample_values": "1, 2, 3"
        },
        "Scholarship_Amount": {
          "data_type": "FLOAT",
          "business_meaning": "Scholarship amount allocated to the student",
          "optimization_purpose": "Decision variable in optimization model",
          "sample_values": "1000.0, 2000.0, 3000.0"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "Total_Budget": {
    "data_type": "FLOAT",
    "business_meaning": "Total budget available for scholarships",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 150000.0,
    "business_justification": "A realistic budget for a university scholarship program, allowing for meaningful allocations."
  },
  "Scholarship_Factor": {
    "data_type": "FLOAT",
    "business_meaning": "Factor to ensure higher GPA students receive more scholarships",
    "optimization_role": "Constraint bound in optimization model",
    "configuration_type": "scalar_parameter",
    "value": 1000.0,
    "business_justification": "A factor that ensures higher GPA students receive significantly more scholarships, aligning with academic priorities."
  }
}

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: game_1

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: Scholarship_Amount[i] (continuous)
- Operational parameters align with expected linear objective: maximize ∑(w1 * GPA[i] + w2 * HoursPerWeek[i] + w3 * Hours_Played[i])
- Business configuration includes: Total budget available for scholarships (used for Constraint bound in optimization model), Factor to ensure higher GPA students receive more scholarships (used for Constraint bound 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 ∑(w1 * GPA[i] + w2 * HoursPerWeek[i] + w3 * Hours_Played[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: ['∑(Scholarship_Amount[i]) ≤ Total_Budget', 'Scholarship_Amount[i] ≥ Scholarship_Factor * GPA[i]', 'Min_Hours_Sports[i] ≤ HoursPerWeek[i] ≤ Max_Hours_Sports[i]', 'Min_Hours_Gaming[i] ≤ Hours_Played[i] ≤ Max_Hours_Gaming[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 3 Database Schema
-- Objective: Schema changes include adding missing optimization requirements to business configuration logic and ensuring all mappings are complete.

CREATE TABLE Academic_Performance (
  Student_ID INTEGER,
  GPA FLOAT
);

CREATE TABLE Objective_Weights (
  w1 FLOAT,
  w2 FLOAT,
  w3 FLOAT
);

CREATE TABLE SportsInfo (
  Student_ID INTEGER,
  HoursPerWeek FLOAT,
  Min_Hours_Sports FLOAT,
  Max_Hours_Sports FLOAT
);

CREATE TABLE Plays_Games (
  Student_ID INTEGER,
  Hours_Played FLOAT,
  Min_Hours_Gaming FLOAT,
  Max_Hours_Gaming FLOAT
);

CREATE TABLE Scholarship_Allocation (
  Student_ID INTEGER,
  Scholarship_Amount 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 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic university scholarship allocation scenarios, considering typical GPA ranges, sports and gaming participation hours, and budget constraints.

-- Realistic data for Academic_Performance
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (1, 3.8);
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (2, 3.5);
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (3, 3.2);

-- Realistic data for Objective_Weights
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.6, 0.25, 0.15);
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.5, 0.3, 0.2);
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.4, 0.35, 0.25);

-- Realistic data for SportsInfo
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (1, 10.0, 2.0, 15.0);
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (2, 7.5, 2.5, 18.0);
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (3, 5.0, 3.0, 20.0);

-- Realistic data for Plays_Games
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (1, 12.5, 5.0, 20.0);
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (2, 15.0, 6.0, 25.0);
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (3, 10.0, 5.5, 22.0);

-- Realistic data for Scholarship_Allocation
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (1, 3000.0);
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (2, 2000.0);
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (3, 1000.0);


```

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

Response:
# Complete Optimization Problem and Solution: game_1

## 1. Problem Context and Goals

### Context  
A university is tasked with optimizing the allocation of scholarships to students based on three key factors: academic performance, sports participation, and gaming habits. The goal is to maximize overall student satisfaction and performance while adhering to budget constraints and ensuring fairness in scholarship distribution. The university has a total budget of $150,000 available for scholarships, and a factor of 1000 is applied to ensure that students with higher GPAs receive proportionally more scholarships.  

The decision variables in this problem are the scholarship amounts allocated to each student, which are continuous values. The operational parameters include the weights assigned to academic performance (GPA), sports participation (hours per week), and gaming habits (hours played). These weights are used to calculate a weighted sum that represents the overall satisfaction and performance of students.  

The problem is designed to avoid nonlinear relationships, ensuring that all calculations and constraints are linear. For example, the scholarship amount for each student is directly proportional to their GPA, and the total scholarship allocation must not exceed the available budget. Additionally, students must meet minimum and maximum hour requirements for both sports participation and gaming to be eligible for scholarships.  

### Goals  
The primary goal of this optimization problem is to maximize the total weighted sum of student satisfaction, which is influenced by academic performance, sports participation, and gaming habits. Success is measured by how well the scholarship allocations align with the weighted contributions of these factors.  

The optimization aims to ensure that students with higher GPAs receive more scholarships, while also considering their involvement in sports and gaming. The weights assigned to each factor (GPA, sports participation, and gaming habits) are critical in determining the final allocation. The university seeks to achieve a fair and balanced distribution of scholarships that encourages both academic excellence and extracurricular engagement.  

## 2. Constraints  

The optimization problem is subject to the following constraints:  
1. **Total Budget Constraint**: The sum of all scholarship amounts allocated to students must not exceed the total budget of $150,000.  
2. **Scholarship Fairness Constraint**: Each student's scholarship amount must be at least proportional to their GPA, using a factor of 1000 to ensure higher GPA students receive more scholarships.  
3. **Sports Participation Constraints**: Each student must meet the minimum and maximum hour requirements for sports participation. These requirements ensure that students are actively engaged in sports without overcommitting.  
4. **Gaming Habits Constraints**: Each student must meet the minimum and maximum hour requirements for gaming. These requirements ensure that students maintain a balanced lifestyle while still enjoying gaming activities.  

These constraints are designed to ensure that the scholarship allocations are fair, feasible, and aligned with the university's priorities.  

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 3 Database Schema
-- Objective: Schema changes include adding missing optimization requirements to business configuration logic and ensuring all mappings are complete.

CREATE TABLE Academic_Performance (
  Student_ID INTEGER,
  GPA FLOAT
);

CREATE TABLE Objective_Weights (
  w1 FLOAT,
  w2 FLOAT,
  w3 FLOAT
);

CREATE TABLE SportsInfo (
  Student_ID INTEGER,
  HoursPerWeek FLOAT,
  Min_Hours_Sports FLOAT,
  Max_Hours_Sports FLOAT
);

CREATE TABLE Plays_Games (
  Student_ID INTEGER,
  Hours_Played FLOAT,
  Min_Hours_Gaming FLOAT,
  Max_Hours_Gaming FLOAT
);

CREATE TABLE Scholarship_Allocation (
  Student_ID INTEGER,
  Scholarship_Amount FLOAT
);
```

### Data Dictionary  
- **Academic_Performance**:  
  - **Student_ID**: Unique identifier for each student.  
  - **GPA**: Grade Point Average of the student, used to determine academic performance and scholarship allocation.  

- **Objective_Weights**:  
  - **w1**: Weight assigned to academic performance in the objective function.  
  - **w2**: Weight assigned to sports participation in the objective function.  
  - **w3**: Weight assigned to gaming habits in the objective function.  

- **SportsInfo**:  
  - **Student_ID**: Unique identifier for each student.  
  - **HoursPerWeek**: Hours spent on sports per week, used in the objective function and constraints.  
  - **Min_Hours_Sports**: Minimum hours required for sports participation, used as a constraint bound.  
  - **Max_Hours_Sports**: Maximum hours allowed for sports participation, used as a constraint bound.  

- **Plays_Games**:  
  - **Student_ID**: Unique identifier for each student.  
  - **Hours_Played**: Hours spent on gaming per week, used in the objective function and constraints.  
  - **Min_Hours_Gaming**: Minimum hours required for gaming, used as a constraint bound.  
  - **Max_Hours_Gaming**: Maximum hours allowed for gaming, used as a constraint bound.  

- **Scholarship_Allocation**:  
  - **Student_ID**: Unique identifier for each student.  
  - **Scholarship_Amount**: Scholarship amount allocated to the student, which is the decision variable in the optimization model.  

### Current Stored Values  
```sql
-- Iteration 3 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic university scholarship allocation scenarios, considering typical GPA ranges, sports and gaming participation hours, and budget constraints.

-- Realistic data for Academic_Performance
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (1, 3.8);
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (2, 3.5);
INSERT INTO Academic_Performance (Student_ID, GPA) VALUES (3, 3.2);

-- Realistic data for Objective_Weights
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.6, 0.25, 0.15);
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.5, 0.3, 0.2);
INSERT INTO Objective_Weights (w1, w2, w3) VALUES (0.4, 0.35, 0.25);

-- Realistic data for SportsInfo
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (1, 10.0, 2.0, 15.0);
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (2, 7.5, 2.5, 18.0);
INSERT INTO SportsInfo (Student_ID, HoursPerWeek, Min_Hours_Sports, Max_Hours_Sports) VALUES (3, 5.0, 3.0, 20.0);

-- Realistic data for Plays_Games
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (1, 12.5, 5.0, 20.0);
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (2, 15.0, 6.0, 25.0);
INSERT INTO Plays_Games (Student_ID, Hours_Played, Min_Hours_Gaming, Max_Hours_Gaming) VALUES (3, 10.0, 5.5, 22.0);

-- Realistic data for Scholarship_Allocation
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (1, 3000.0);
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (2, 2000.0);
INSERT INTO Scholarship_Allocation (Student_ID, Scholarship_Amount) VALUES (3, 1000.0);
```
