To solve this optimization problem, we first need to translate the natural language description into a symbolic representation. Let's denote:

- $x_1$ as the number of individual cereal boxes made,
- $x_2$ as the number of family size cereal boxes made.

The objective function is to maximize profit. Given that the profit per individual cereal box is $4 and the profit per family size cereal box is $8, the objective function can be represented algebraically as:

\[ \text{Maximize:} \quad 4x_1 + 8x_2 \]

The constraints based on the availability of cereal units and filling time are:

1. Cereal units constraint: Each individual cereal box takes 20 units of cereal, and each family size cereal box takes 60 units. The company has 2000 units available.
\[ 20x_1 + 60x_2 \leq 2000 \]
2. Filling time constraint: It takes 10 minutes to fill an individual cereal box and 15 minutes for a family size cereal box. The company has 750 minutes available.
\[ 10x_1 + 15x_2 \leq 750 \]

Additionally, we must consider non-negativity constraints since the number of boxes cannot be negative:

\[ x_1 \geq 0, \quad x_2 \geq 0 \]

In symbolic notation with natural language objects, our problem description becomes:
```json
{
  'sym_variables': [('x1', 'individual cereal boxes'), ('x2', 'family size cereal boxes')],
  'objective_function': '4*x1 + 8*x2',
  'constraints': ['20*x1 + 60*x2 <= 2000', '10*x1 + 15*x2 <= 750', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="individual_cereal_boxes")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="family_size_cereal_boxes")

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

# Add constraints
m.addConstr(20*x1 + 60*x2 <= 2000, "cereal_units")
m.addConstr(10*x1 + 15*x2 <= 750, "filling_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Individual cereal boxes: {x1.x}")
    print(f"Family size cereal boxes: {x2.x}")
    print(f"Maximum profit: ${4*x1.x + 8*x2.x}")
else:
    print("No optimal solution found")
```