To solve the given optimization problem, we first need to define the symbolic representation of the variables and the objective function, followed by the list of constraints. The variables in this problem are 'knishes' and 'kiwis', which can be represented symbolically as $x_1$ and $x_2$, respectively.

The objective function aims to maximize the value of $4 \cdot x_1 + 8 \cdot x_2$, where $x_1$ represents the number of knishes and $x_2$ represents the number of kiwis.

Given the constraints:
- Each knish contains 22 grams of carbohydrates, and each kiwi contains 28 grams.
- Each knish contains 14 milligrams of calcium, and each kiwi contains 10 milligrams.
- The total carbohydrates from knishes and kiwis must be at least 21 grams and at most 49 grams (which is repeated as two separate constraints but essentially means the same).
- The total calcium from knishes and kiwis must be at least 40 milligrams and at most 77 milligrams.
- $9x_1 - 3x_2 \geq 0$.
- $x_1$ must be an integer, and $x_2$ can be a non-integer.

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'knishes'), ('x2', 'kiwis')],
    'objective_function': 'Maximize 4*x1 + 8*x2',
    'constraints': [
        '22*x1 + 28*x2 >= 21', 
        '22*x1 + 28*x2 <= 49', 
        '14*x1 + 10*x2 >= 40', 
        '14*x1 + 10*x2 <= 77', 
        '9*x1 - 3*x2 >= 0'
    ]
}
```

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

```python
from gurobipy import *

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

# Add variables to the model: x1 (knishes) is an integer variable, and x2 (kiwis) is a continuous variable
x1 = m.addVar(vtype=GRB.INTEGER, name="knishes")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="kiwis")

# Set the objective function: Maximize 4*x1 + 8*x2
m.setObjective(4*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints to the model
m.addConstr(22*x1 + 28*x2 >= 21, "carb_min")
m.addConstr(22*x1 + 28*x2 <= 49, "carb_max")
m.addConstr(14*x1 + 10*x2 >= 40, "calcium_min")
m.addConstr(14*x1 + 10*x2 <= 77, "calcium_max")
m.addConstr(9*x1 - 3*x2 >= 0, "misc_constraint")

# Optimize the model
m.optimize()

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