To solve Jason's problem, we first need to define the symbolic representation of the optimization 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 function is to minimize the total cost. Given that the sports drink costs $5 per bottle and coconut water costs $3 per bottle, the objective function can be written as:
\[ \text{Minimize} \quad 5x_1 + 3x_2 \]

The constraints are based on Jason's nutritional needs:
- At least 10 units of calcium: $x_1 + 4x_2 \geq 10$ (since sports drink contains 1 unit of calcium per bottle and coconut water contains 4 units of calcium per bottle).
- At least 15 units of potassium: $2x_1 + x_2 \geq 15$ (since sports drink contains 2 units of potassium per bottle and coconut water contains 1 unit of potassium per bottle).
- At least 13 units of magnesium: $3x_1 + 2x_2 \geq 13$ (since sports drink contains 3 units of magnesium per bottle and coconut water contains 2 units of magnesium per bottle).

Additionally, Jason cannot drink a negative number of bottles, so we have:
- $x_1 \geq 0$
- $x_2 \geq 0$

The symbolic representation in the requested format is:
```json
{
  'sym_variables': [('x1', 'number of bottles of sports drink'), ('x2', 'number of bottles of coconut water')],
  'objective_function': '5*x1 + 3*x2',
  'constraints': ['x1 + 4*x2 >= 10', '2*x1 + x2 >= 15', '3*x1 + 2*x2 >= 13', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's write the Gurobi code to solve this linear programming problem:

```python
from gurobipy import *

# Create a new model
m = Model("Jason_Nutrition")

# Create variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="sports_drink")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="coconut_water")

# Set the objective function
m.setObjective(5*x1 + 3*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(x1 + 4*x2 >= 10, "calcium")
m.addConstr(2*x1 + x2 >= 15, "potassium")
m.addConstr(3*x1 + 2*x2 >= 13, "magnesium")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Sports drink bottles: {x1.x}")
    print(f"Coconut water bottles: {x2.x}")
    print(f"Total cost: ${5*x1.x + 3*x2.x:.2f}")
else:
    print("No optimal solution found")
```