## Step 1: Define the symbolic representation of the variables
The variables are 'military intelligence companies', 'transportation companies', and 'water purification units'. Let's denote them as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $3.34x_0 + 7.58x_1 + 8.16x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $0.9x_0 + 5.21x_2 \geq 31$
- $0.9x_0 + 2.23x_1 \geq 23$
- $2.23x_1 + 5.21x_2 \geq 37$
- $0.9x_0 + 2.23x_1 + 5.21x_2 \geq 37$
- $3.14x_0 + 1.42x_1 \geq 28$
- $3.14x_0 + 3.04x_2 \geq 20$
- $1.42x_1 + 3.04x_2 \geq 29$
- $3.14x_0 + 1.42x_1 + 3.04x_2 \geq 29$
- $3.14x_0 + 1.42x_1 \leq 45$

## 4: Convert the problem into a Gurobi model
We will use Gurobi's Python API to model and solve this problem.

## 5: Write the Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name='military_intelligence_companies', vtype=gurobi.GRB.INTEGER)
x1 = model.addVar(name='transportation_companies', vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name='water_purification_units', vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(3.34*x0 + 7.58*x1 + 8.16*x2, gurobi.GRB.MINIMIZE)

# Define the constraints
model.addConstr(0.9*x0 + 5.21*x2 >= 31, name='offensive_capability_rating_1')
model.addConstr(0.9*x0 + 2.23*x1 >= 23, name='offensive_capability_rating_2')
model.addConstr(2.23*x1 + 5.21*x2 >= 37, name='offensive_capability_rating_3')
model.addConstr(0.9*x0 + 2.23*x1 + 5.21*x2 >= 37, name='offensive_capability_rating_4')
model.addConstr(3.14*x0 + 1.42*x1 >= 28, name='deployment_weight_1')
model.addConstr(3.14*x0 + 3.04*x2 >= 20, name='deployment_weight_2')
model.addConstr(1.42*x1 + 3.04*x2 >= 29, name='deployment_weight_3')
model.addConstr(3.14*x0 + 1.42*x1 + 3.04*x2 >= 29, name='deployment_weight_4')
model.addConstr(3.14*x0 + 1.42*x1 <= 45, name='deployment_weight_5')

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objVal)
    print('Military intelligence companies: ', x0.varValue)
    print('Transportation companies: ', x1.varValue)
    print('Water purification units: ', x2.varValue)
else:
    print('The model is infeasible')
```

## 6: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'military intelligence companies'), 
        ('x1', 'transportation companies'), 
        ('x2', 'water purification units')
    ], 
    'objective_function': '3.34*x0 + 7.58*x1 + 8.16*x2', 
    'constraints': [
        '0.9*x0 + 5.21*x2 >= 31', 
        '0.9*x0 + 2.23*x1 >= 23', 
        '2.23*x1 + 5.21*x2 >= 37', 
        '0.9*x0 + 2.23*x1 + 5.21*x2 >= 37', 
        '3.14*x0 + 1.42*x1 >= 28', 
        '3.14*x0 + 3.04*x2 >= 20', 
        '1.42*x1 + 3.04*x2 >= 29', 
        '3.14*x0 + 1.42*x1 + 3.04*x2 >= 29', 
        '3.14*x0 + 1.42*x1 <= 45'
    ]
}
```