To solve the optimization problem described, we need to first translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the given information.

Let's denote:
- $x_1$ as the number of bananas,
- $x_2$ as the number of eggs,
- $x_3$ as the number of rotisserie chickens.

The objective function to minimize is: $7x_1 + 4x_2 + 9x_3$.

The constraints are:
1. Calcium from bananas and rotisserie chickens: $18x_1 + 6x_3 \geq 18$.
2. Calcium from eggs and rotisserie chickens: $3x_2 + 6x_3 \geq 18$.
3. Calcium from all sources: $18x_1 + 3x_2 + 6x_3 \geq 18$.
4. Bananas and rotisserie chickens constraint: $4x_1 - 6x_3 \geq 0$.
5. Eggs and rotisserie chickens constraint: $8x_2 - 9x_3 \geq 0$.

All variables can be non-integer, meaning they are continuous.

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'bananas'), ('x2', 'eggs'), ('x3', 'rotisserie chickens')],
    'objective_function': '7*x1 + 4*x2 + 9*x3',
    'constraints': [
        '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'
    ]
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name='bananas', lb=0)  # Number of bananas
x2 = m.addVar(name='eggs', lb=0)     # Number of eggs
x3 = m.addVar(name='rotisserie_chickens', lb=0)  # Number of rotisserie chickens

# Define the objective function
m.setObjective(7*x1 + 4*x2 + 9*x3, GRB.MINIMIZE)

# Add constraints
m.addConstr(18*x1 + 6*x3 >= 18, name='calcium_from_bananas_and_chickens')
m.addConstr(3*x2 + 6*x3 >= 18, name='calcium_from_eggs_and_chickens')
m.addConstr(18*x1 + 3*x2 + 6*x3 >= 18, name='total_calcium')
m.addConstr(4*x1 - 6*x3 >= 0, name='bananas_and_chickens_constraint')
m.addConstr(8*x2 - 9*x3 >= 0, name='eggs_and_chickens_constraint')

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Bananas: {x1.x}")
    print(f"Eggs: {x2.x}")
    print(f"Rotisserie Chickens: {x3.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```