## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the amount of drug A in mg.
- $x_2$ represents the amount of drug B in mg.

## Step 2: Formulate the objective function
The objective is to minimize the cost of the mixture. The cost of drug A is $0.50 per mg, and the cost of drug B is $0.30 per mg. Therefore, the objective function can be represented as:
\[ \text{Minimize:} \quad 0.50x_1 + 0.30x_2 \]

## 3: Define the constraints
The mixture must contain at least 5 units of pain killer and 12 units of fever reliever.
- The amount of pain killer in drug A is 3 units/mg, and in drug B is 2 units/mg. So, the pain killer constraint is: $3x_1 + 2x_2 \geq 5$.
- The amount of fever reliever in drug A is 2.5 units/mg, and in drug B is 3.5 units/mg. So, the fever reliever constraint is: $2.5x_1 + 3.5x_2 \geq 12$.
Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the amounts of drugs cannot be negative.

## 4: Symbolic representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'amount of drug A in mg'), ('x2', 'amount of drug B in mg')],
    'objective_function': '0.50*x1 + 0.30*x2',
    'constraints': [
        '3*x1 + 2*x2 >= 5',
        '2.5*x1 + 3.5*x2 >= 12',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## 5: Gurobi code
Now, let's write the Gurobi code in Python to solve this linear programming problem:
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="x1")  # amount of drug A
    x2 = model.addVar(lb=0, name="x2")  # amount of drug B

    # Define the objective function
    model.setObjective(0.50 * x1 + 0.30 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(3 * x1 + 2 * x2 >= 5, name="pain_killer_constraint")
    model.addConstr(2.5 * x1 + 3.5 * x2 >= 12, name="fever_reliever_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Amount of drug A: {x1.varValue} mg")
        print(f"Amount of drug B: {x2.varValue} mg")
        print(f"Total cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_lp()
```