To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each item (corn cobs and chicken breasts), formulating the objective function using these variables, and then listing all constraints in terms of these symbolic variables.

Let's denote:
- \(x_1\) as the number of corn cobs,
- \(x_2\) as the number of chicken breasts.

The objective function to minimize is given by \(3x_1 + 7x_2\).

Now, let's translate the constraints into algebraic expressions using our symbolic variables:

1. Fat constraint from corn cobs: \(17x_1\)
2. Carbohydrates constraint from corn cobs: \(22x_1\)
3. Fat constraint from chicken breasts: \(4x_2\)
4. Carbohydrates constraint from chicken breasts: \(18x_2\)

Given constraints:
- At least 16 grams of fat: \(17x_1 + 4x_2 \geq 16\)
- At least 52 grams of carbohydrates: \(22x_1 + 18x_2 \geq 52\)
- Minimum constraint: \(-7x_1 + 10x_2 \geq 0\)
- Maximum fat constraint: \(17x_1 + 4x_2 \leq 69\)
- Maximum carbohydrates constraint: \(22x_1 + 18x_2 \leq 210\)

Since both corn cobs and chicken breasts must be used in whole numbers, we also have:
- \(x_1\) is an integer,
- \(x_2\) is an integer.

Therefore, our symbolic representation of the problem can be summarized as follows:

```json
{
    'sym_variables': [('x1', 'corn cobs'), ('x2', 'chicken breasts')],
    'objective_function': '3*x1 + 7*x2',
    'constraints': [
        '17*x1 + 4*x2 >= 16',
        '22*x1 + 18*x2 >= 52',
        '-7*x1 + 10*x2 >= 0',
        '17*x1 + 4*x2 <= 69',
        '22*x1 + 18*x2 <= 210'
    ]
}
```

Here is the Gurobi code to solve this problem:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(vtype=GRB.INTEGER, name="corn_cobs")
x2 = m.addVar(vtype=GRB.INTEGER, name="chicken_breasts")

# Set the objective function
m.setObjective(3*x1 + 7*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(17*x1 + 4*x2 >= 16, "fat_min")
m.addConstr(22*x1 + 18*x2 >= 52, "carbs_min")
m.addConstr(-7*x1 + 10*x2 >= 0, "min_constraint")
m.addConstr(17*x1 + 4*x2 <= 69, "fat_max")
m.addConstr(22*x1 + 18*x2 <= 210, "carbs_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: x1 = {x1.x}, x2 = {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```