To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for the quantities of Capsule A and Capsule B to be used, formulating the objective function that represents the total cost, and listing the constraints based on the minimum requirements for targeted medicine, pain reliever, and filler.

Let's denote:
- \(x_1\) as the number of Capsule A used,
- \(x_2\) as the number of Capsule B used.

The objective is to minimize the total cost. Given that the cost per capsule A is $2 and the cost per capsule B is $3, the objective function can be represented as:
\[ \text{Minimize:} \quad 2x_1 + 3x_2 \]

The constraints are based on the minimum requirements for each component:
- Targeted medicine: \(2x_1 + 3x_2 \geq 20\),
- Pain reliever: \(3x_1 + x_2 \geq 20\),
- Filler: \(x_1 + 3x_2 \geq 15\).

Also, since we cannot use a negative number of capsules, we have:
- \(x_1 \geq 0\),
- \(x_2 \geq 0\).

Thus, the symbolic representation of the problem is:

```json
{
  'sym_variables': [('x1', 'Number of Capsule A'), ('x2', 'Number of Capsule B')],
  'objective_function': '2*x1 + 3*x2',
  'constraints': [
    '2*x1 + 3*x2 >= 20', 
    '3*x1 + x2 >= 20', 
    'x1 + 3*x2 >= 15', 
    'x1 >= 0', 
    'x2 >= 0'
  ]
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Capsule_A")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Capsule_B")

# Set the objective function
m.setObjective(2*x1 + 3*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x1 + 3*x2 >= 20, "Targeted_Medicine")
m.addConstr(3*x1 + x2 >= 20, "Pain_Reliever")
m.addConstr(x1 + 3*x2 >= 15, "Filler")

# Optimize the model
m.optimize()

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