To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of medication A and B to be mixed, formulating the objective function that represents the total cost, and establishing the constraints based on the required amounts of cough relief, pain relief, and fever relief.

Let's define:
- $x_1$ as the number of units of medication A to be mixed.
- $x_2$ as the number of units of medication B to be mixed.

The objective function aims to minimize the total cost. Given that the cost per unit of medication A is $1 and the cost per unit of medication B is $2, the objective function can be represented algebraically as:
\[ \text{Minimize} \quad x_1 + 2x_2 \]

The constraints are based on the minimum requirements for each type of relief:
- Cough relief: $1x_1 + 3x_2 \geq 20$
- Pain relief: $2x_1 + 1x_2 \geq 25$
- Fever relief: $3x_1 + 2x_2 \geq 30$

Additionally, since we cannot have negative quantities of medications, we also have:
- $x_1 \geq 0$
- $x_2 \geq 0$

In symbolic notation with natural language objects, the problem can be represented as:
```json
{
    'sym_variables': [('x1', 'units of medication A'), ('x2', 'units of medication B')],
    'objective_function': 'Minimize x1 + 2*x2',
    'constraints': [
        'x1 + 3*x2 >= 20',
        '2*x1 + x2 >= 25',
        '3*x1 + 2*x2 >= 30',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

To solve this problem using Gurobi in Python, we'll use the following code:

```python
from gurobipy import *

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

# Add variables to the model
x1 = m.addVar(name="med_A", vtype=GRB.CONTINUOUS, lb=0)
x2 = m.addVar(name="med_B", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function
m.setObjective(x1 + 2*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(x1 + 3*x2 >= 20, name="cough_relief")
m.addConstr(2*x1 + x2 >= 25, name="pain_relief")
m.addConstr(3*x1 + 2*x2 >= 30, name="fever_relief")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Medication A:", x1.x)
    print("Medication B:", x2.x)
    print("Total Cost:", m.objVal)
else:
    print("No optimal solution found.")
```