## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'chicken drumsticks' and 'hamburgers', which we can denote as $x_1$ and $x_2$ respectively. The objective function to minimize is $4x_1 + 3x_2$. The constraints are as follows:
- $9x_1 + 3x_2 \geq 24$ (carbohydrates)
- $3x_1 + 5x_2 \geq 13$ (tastiness rating)
- $14x_1 + 6x_2 \geq 16$ (protein)
- $11x_1 + x_2 \geq 18$ (calcium)
- $-6x_1 + 3x_2 \geq 0$ (linear combination)
- $9x_1 + 3x_2 \leq 33$ (carbohydrates upper bound)
- $3x_1 + 5x_2 \leq 37$ (tastiness rating upper bound)
- $14x_1 + 6x_2 \leq 36$ (protein upper bound)
- $11x_1 + x_2 \leq 33$ (calcium upper bound)
- $x_1$ is an integer (nonfractional number of chicken drumsticks)
- $x_2$ can be fractional (amount of hamburgers)

## Step 2: Convert the problem into a Gurobi-compatible format
We need to define the variables, the objective function, and the constraints in a way that Gurobi can understand.

## 3: Write the Gurobi code
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="chicken_drumsticks", vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name="hamburgers")

# Set the objective function
model.setObjective(4 * x1 + 3 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(9 * x1 + 3 * x2 >= 24, name="carbohydrates_min")
model.addConstr(3 * x1 + 5 * x2 >= 13, name="tastiness_rating_min")
model.addConstr(14 * x1 + 6 * x2 >= 16, name="protein_min")
model.addConstr(11 * x1 + x2 >= 18, name="calcium_min")
model.addConstr(-6 * x1 + 3 * x2 >= 0, name="linear_combination")
model.addConstr(9 * x1 + 3 * x2 <= 33, name="carbohydrates_max")
model.addConstr(3 * x1 + 5 * x2 <= 37, name="tastiness_rating_max")
model.addConstr(14 * x1 + 6 * x2 <= 36, name="protein_max")
model.addConstr(11 * x1 + x2 <= 33, name="calcium_max")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Chicken drumsticks: ", x1.varValue)
    print("Hamburgers: ", x2.varValue)
else:
    print("The model is infeasible")
```

## Step 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'chicken drumsticks'), ('x2', 'hamburgers')],
    'objective_function': '4*x1 + 3*x2',
    'constraints': [
        '9*x1 + 3*x2 >= 24',
        '3*x1 + 5*x2 >= 13',
        '14*x1 + 6*x2 >= 16',
        '11*x1 + x2 >= 18',
        '-6*x1 + 3*x2 >= 0',
        '9*x1 + 3*x2 <= 33',
        '3*x1 + 5*x2 <= 37',
        '14*x1 + 6*x2 <= 36',
        '11*x1 + x2 <= 33'
    ]
}
```