To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's denote:
- $x_1$ as the number of Protein Bar A to buy,
- $x_2$ as the number of Protein Bar B to buy.

The objective is to minimize the total cost, which can be represented as $7x_1 + 10x_2$, since each Protein Bar A costs $7 and each Protein Bar B costs $10.

The constraints are based on the nutritional requirements:
- Minimum 80 grams of protein: $10x_1 + 15x_2 \geq 80$,
- Minimum 50 grams of fat: $3x_1 + 5x_2 \geq 50$,
- Minimum 100 grams of carbs: $11x_1 + 8x_2 \geq 100$.

Also, since we cannot buy a negative number of bars, we have:
- $x_1 \geq 0$ and $x_2 \geq 0$.

The symbolic representation of the problem is thus:

```json
{
    'sym_variables': [('x1', 'Protein Bar A'), ('x2', 'Protein Bar B')],
    'objective_function': '7*x1 + 10*x2',
    'constraints': ['10*x1 + 15*x2 >= 80', '3*x1 + 5*x2 >= 50', '11*x1 + 8*x2 >= 100', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this linear programming problem, we can use Gurobi in Python. Here is how you would set it up:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(7*x1 + 10*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(10*x1 + 15*x2 >= 80, "protein")
m.addConstr(3*x1 + 5*x2 >= 50, "fat")
m.addConstr(11*x1 + 8*x2 >= 100, "carbs")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Buy {x1.x} of Protein Bar A")
    print(f"Buy {x2.x} of Protein Bar B")
    print(f"Total cost: ${7*x1.x + 10*x2.x}")
else:
    print("No optimal solution found")

```