## Step 1: Define the symbolic representation of the variables
The variables are 'corn cobs' and 'chicken breasts', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $3x_1 + 7x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $17x_1 + 4x_2 \geq 16$ (at least 16 grams of fat)
- $22x_1 + 18x_2 \geq 52$ (at least 52 grams of carbohydrates)
- $-7x_1 + 10x_2 \geq 0$
- $17x_1 + 4x_2 \leq 69$ (no more than 69 grams of fat)
- $22x_1 + 18x_2 \leq 210$ (up to 210 grams of carbohydrates)

## 4: Consider the integer constraints
- $x_1$ must be an integer (whole number of corn cobs)
- $x_2$ must be an integer (whole number of chicken breasts)

## 5: Write down the symbolic representation of the problem
```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'
]
}
```

## 6: Convert the problem into Gurobi code
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name='corn_cobs', vtype=gurobi.GRB.INTEGER)  # corn cobs
x2 = m.addVar(name='chicken_breasts', vtype=gurobi.GRB.INTEGER)  # chicken breasts

# Objective function
m.setObjective(3*x1 + 7*x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(17*x1 + 4*x2 >= 16, name='fat_min')
m.addConstr(22*x1 + 18*x2 >= 52, name='carb_min')
m.addConstr(-7*x1 + 10*x2 >= 0, name='linear_constraint')
m.addConstr(17*x1 + 4*x2 <= 69, name='fat_max')
m.addConstr(22*x1 + 18*x2 <= 210, name='carb_max')

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Corn cobs: ', x1.varValue)
    print('Chicken breasts: ', x2.varValue)
else:
    print('The model is infeasible')
```