To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints in terms of these variables.

Let's denote:
- $x_1$ as the number of chickens the cyclist should buy.
- $x_2$ as the number of potatoes the cyclist should buy.

The objective is to minimize the total cost, which can be represented by the objective function: $6x_1 + 2x_2$.

The constraints based on the nutritional requirements are:
1. Protein: $20x_1 + 2x_2 \geq 80$
2. Fat: $4x_1 + 3x_2 \geq 50$
3. Carbs: $4x_1 + 7x_2 \geq 100$

Additionally, since the cyclist cannot buy a negative number of chickens or potatoes, we have:
4. Non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$.

Thus, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of chickens'), ('x2', 'number of potatoes')],
    'objective_function': '6*x1 + 2*x2',
    'constraints': ['20*x1 + 2*x2 >= 80', '4*x1 + 3*x2 >= 50', '4*x1 + 7*x2 >= 100', '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("Cyclist_Diet")

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

# Set the objective function
m.setObjective(6*x1 + 2*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(20*x1 + 2*x2 >= 80, "protein")
m.addConstr(4*x1 + 3*x2 >= 50, "fat")
m.addConstr(4*x1 + 7*x2 >= 100, "carbs")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Buy {x1.x} chickens")
    print(f"Buy {x2.x} potatoes")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")

```