# Complete Optimization Problem and Solution: election_representative

## 1. Problem Context and Goals

### Context  
A political party is strategically planning the allocation of its campaign resources to maximize the number of seats won in upcoming elections. The party's decision-making process involves determining the level of effort to allocate to each representative's campaign. This effort is represented as a continuous variable for each representative. The primary objective is to maximize the overall effectiveness of these efforts, which is directly linked to the number of seats each representative can potentially secure. The party operates under a fixed total budget for campaign resources, which serves as a constraint on the total effort that can be distributed. Each representative's campaign also has specific minimum and maximum effort requirements, ensuring that resources are allocated efficiently and effectively. The business configuration includes the total campaign resources available for allocation, which is a critical parameter in this optimization process.

### Goals  
The optimization goal is to maximize the total number of seats won by the party. This is achieved by optimizing the allocation of campaign efforts across representatives. The metric for success is the maximization of the sum of the product of seats associated with each representative and the effort allocated to them. This goal is articulated in natural language to emphasize the linear relationship between effort allocation and seat maximization, without resorting to mathematical notation.

## 2. Constraints    

The optimization process is subject to several constraints that ensure the feasibility and effectiveness of the resource allocation:

- The total effort allocated across all representatives must not exceed the total campaign resources available. This constraint ensures that the party operates within its budgetary limits.
- Each representative's campaign effort must fall within specified minimum and maximum bounds. This ensures that each campaign receives a sufficient level of support while preventing over-allocation of resources.

These constraints are described in business terms that naturally align with linear mathematical forms, avoiding any nonlinear relationships.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating new tables for missing optimization data and updating configuration logic for scalar parameters and formulas.

CREATE TABLE election (
  Seats INTEGER,
  Minimum_Effort FLOAT,
  Maximum_Effort FLOAT
);

CREATE TABLE representative_effort (
  Effort FLOAT
);
```

### Data Dictionary  
The data dictionary provides a comprehensive mapping of tables and columns to their business purposes and roles in the optimization process:

- **Election Table**: This table stores data related to each representative's potential election outcomes.
  - **Seats**: Represents the number of seats associated with each representative. This serves as the objective coefficient in the optimization process.
  - **Minimum Effort**: Indicates the minimum level of effort required for each representative's campaign. This acts as a lower bound constraint.
  - **Maximum Effort**: Specifies the maximum level of effort allowed for each representative's campaign. This serves as an upper bound constraint.

- **Representative Effort Table**: This table captures the level of campaign effort allocated to each representative.
  - **Effort**: Represents the decision variable in the optimization process, indicating the level of effort allocated to each representative's campaign.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical campaign resource allocations and historical performance metrics to ensure a realistic and solvable optimization problem.

-- Realistic data for election
INSERT INTO election (Seats, Minimum_Effort, Maximum_Effort) VALUES (1, 10.0, 50.0);
INSERT INTO election (Seats, Minimum_Effort, Maximum_Effort) VALUES (2, 15.0, 60.0);
INSERT INTO election (Seats, Minimum_Effort, Maximum_Effort) VALUES (3, 20.0, 70.0);

-- Realistic data for representative_effort
INSERT INTO representative_effort (Effort) VALUES (20.0);
INSERT INTO representative_effort (Effort) VALUES (30.0);
INSERT INTO representative_effort (Effort) VALUES (40.0);
```