## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milligrams of vitamin B1' and 'milligrams of vitamin B12'. Let's denote 'milligrams of vitamin B1' as $x_1$ and 'milligrams of vitamin B12' as $x_2$. The objective function to maximize is $9.48x_1 + 7.02x_2$. The constraints are:
1. $5x_1 + 6x_2 \geq 38$
2. $-3x_1 + 5x_2 \geq 0$
3. $5x_1 + 6x_2 \leq 82$
4. $x_1, x_2 \geq 0$ (Implicit, as they represent quantities of vitamins)

## Step 2: Convert the problem into a symbolic representation
The symbolic variables are:
- $x_1$ for 'milligrams of vitamin B1'
- $x_2$ for 'milligrams of vitamin B12'

The objective function is: $9.48x_1 + 7.02x_2$

The constraints are:
1. $5x_1 + 6x_2 \geq 38$
2. $-3x_1 + 5x_2 \geq 0$
3. $5x_1 + 6x_2 \leq 82$

## 3: Express the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin B1'), ('x2', 'milligrams of vitamin B12')],
    'objective_function': '9.48*x1 + 7.02*x2',
    'constraints': [
        '5*x1 + 6*x2 >= 38',
        '-3*x1 + 5*x2 >= 0',
        '5*x1 + 6*x2 <= 82'
    ]
}
```

## 4: Implement the problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='milligrams_of_vitamin_B1', lb=0)  # lower bound is 0, as it represents a quantity
    x2 = model.addVar(name='milligrams_of_vitamin_B12', lb=0)  # lower bound is 0, as it represents a quantity

    # Define the objective function
    model.setObjective(9.48 * x1 + 7.02 * x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5 * x1 + 6 * x2 >= 38)
    model.addConstr(-3 * x1 + 5 * x2 >= 0)
    model.addConstr(5 * x1 + 6 * x2 <= 82)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'milligrams of vitamin B1: {x1.varValue}')
        print(f'milligrams of vitamin B12: {x2.varValue}')
        print(f'Objective function value: {model.objVal}')
    else:
        print('No optimal solution found.')

solve_optimization_problem()
```