## Step 1: Define the symbolic representation of the variables
The variables are 'bananas', 'eggs', and 'rotisserie chickens', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7 \times \text{bananas} + 4 \times \text{eggs} + 9 \times \text{rotisserie chickens}$. In symbolic terms, this is $7x_1 + 4x_2 + 9x_3$.

## 3: Define the constraints in symbolic representation
The constraints given are:
1. $18x_1 + 3x_2 + 6x_3 \leq 164$ (calcium constraint, assuming an upper bound),
2. $18x_1 + 6x_3 \geq 18$ (at least 18 milligrams of calcium from bananas and rotisserie chickens),
3. $3x_2 + 6x_3 \geq 18$ (at least 18 milligrams of calcium from eggs and rotisserie chickens),
4. $18x_1 + 3x_2 + 6x_3 \geq 18$ (at least 18 milligrams of calcium from all sources),
5. $4x_1 - 6x_3 \geq 0$ (constraint on bananas and rotisserie chickens),
6. $8x_2 - 9x_3 \geq 0$ (constraint on eggs and rotisserie chickens).

## 4: Create a symbolic representation of the problem
The symbolic representation is:
- Variables: $(x_1, \text{bananas}), (x_2, \text{eggs}), (x_3, \text{rotisserie chickens})$
- Objective function: $7x_1 + 4x_2 + 9x_3$
- Constraints:
  1. $18x_1 + 3x_2 + 6x_3 \leq 164$
  2. $18x_1 + 6x_3 \geq 18$
  3. $3x_2 + 6x_3 \geq 18$
  4. $18x_1 + 3x_2 + 6x_3 \geq 18$
  5. $4x_1 - 6x_3 \geq 0$
  6. $8x_2 - 9x_3 \geq 0$

## 5: Implement the problem in Gurobi
```python
import gurobi

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

# Define the variables
bananas = model.addVar(name="bananas", lb=0)  # Non-negative
eggs = model.addVar(name="eggs", lb=0)  # Non-negative
rotisserie_chickens = model.addVar(name="rotisserie_chickens", lb=0)  # Non-negative

# Objective function
model.setObjective(7 * bananas + 4 * eggs + 9 * rotisserie_chickens, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(18 * bananas + 3 * eggs + 6 * rotisserie_chickens <= 164)
model.addConstr(18 * bananas + 6 * rotisserie_chickens >= 18)
model.addConstr(3 * eggs + 6 * rotisserie_chickens >= 18)
model.addConstr(18 * bananas + 3 * eggs + 6 * rotisserie_chickens >= 18)
model.addConstr(4 * bananas - 6 * rotisserie_chickens >= 0)
model.addConstr(8 * eggs - 9 * rotisserie_chickens >= 0)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Bananas: {bananas.varValue}")
    print(f"Eggs: {eggs.varValue}")
    print(f"Rotisserie Chickens: {rotisserie_chickens.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 6: Provide the symbolic representation in the required format
```json
{
    'sym_variables': [('x1', 'bananas'), ('x2', 'eggs'), ('x3', 'rotisserie chickens')],
    'objective_function': '7*x1 + 4*x2 + 9*x3',
    'constraints': [
        '18*x1 + 3*x2 + 6*x3 <= 164',
        '18*x1 + 6*x3 >= 18',
        '3*x2 + 6*x3 >= 18',
        '18*x1 + 3*x2 + 6*x3 >= 18',
        '4*x1 - 6*x3 >= 0',
        '8*x2 - 9*x3 >= 0'
    ]
}
```