## Step 1: Define the symbolic representation of the problem
Let's denote:
- $x_1$ as the number of bottles of sports drink Jason should drink.
- $x_2$ as the number of bottles of coconut water Jason should drink.

The objective is to minimize the cost, which can be represented as $5x_1 + 3x_2$.

## Step 2: Define the constraints based on the nutritional requirements
Jason needs at least 10 units of calcium, 15 units of potassium, and 13 units of magnesium. The sports drink and coconut water contain the following units of each nutrient per bottle:
- Sports drink: 1 calcium, 2 potassium, 3 magnesium.
- Coconut water: 4 calcium, 1 potassium, 2 magnesium.

This gives us the following constraints:
- Calcium: $1x_1 + 4x_2 \geq 10$
- Potassium: $2x_1 + 1x_2 \geq 15$
- Magnesium: $3x_1 + 2x_2 \geq 13$

## 3: Non-negativity constraints
Since Jason cannot drink a negative number of bottles:
- $x_1 \geq 0$
- $x_2 \geq 0$

## 4: Symbolic representation in JSON format
```json
{
    'sym_variables': [('x1', 'sports drink bottles'), ('x2', 'coconut water bottles')],
    'objective_function': '5*x1 + 3*x2',
    'constraints': [
        '1*x1 + 4*x2 >= 10',
        '2*x1 + 1*x2 >= 15',
        '3*x1 + 2*x2 >= 13',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code in Python
```python
import gurobipy as gp

def solve_jason_nutrition_problem():
    # Create a new model
    model = gp.Model("JasonNutrition")

    # Define variables
    x1 = model.addVar(name="sports_drink", lb=0, vtype=gp.GRB.CONTINUOUS)
    x2 = model.addVar(name="coconut_water", lb=0, vtype=gp.GRB.CONTINUOUS)

    # Objective function: minimize cost
    model.setObjective(5*x1 + 3*x2, gp.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x1 + 4*x2 >= 10, name="calcium")
    model.addConstr(2*x1 + x2 >= 15, name="potassium")
    model.addConstr(3*x1 + 2*x2 >= 13, name="magnesium")

    # Solve the model
    model.optimize()

    # Print the results
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal cost: ${model.objVal:.2f}")
        print(f"Bottles of sports drink: {x1.varValue:.2f}")
        print(f"Bottles of coconut water: {x2.varValue:.2f}")
    else:
        print("No optimal solution found.")

solve_jason_nutrition_problem()
```