To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's define:
- \(x_1\) as the number of red bean bags thrown,
- \(x_2\) as the number of blue bean bags thrown.

The objective is to maximize the total points earned from throwing these bean bags, given that each red bean bag is worth 5 points and each blue bean bag is worth 8 points. Thus, the objective function can be written as:
\[ \text{Maximize:} \quad 5x_1 + 8x_2 \]

The constraints based on the problem description are:
1. Throw at least 3 red bean bags: \( x_1 \geq 3 \)
2. Throw at least 2 blue bean bags: \( x_2 \geq 2 \)
3. Throw at most 8 of either type of bean bag: \( x_1 \leq 8 \) and \( x_2 \leq 8 \)
4. In total, throw 12 bean bags: \( x_1 + x_2 = 12 \)

All variables are non-negative since you cannot throw a negative number of bean bags.

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of red bean bags'), ('x2', 'number of blue bean bags')],
    'objective_function': '5*x1 + 8*x2',
    'constraints': ['x1 >= 3', 'x2 >= 2', 'x1 <= 8', 'x2 <= 8', 'x1 + x2 == 12']
}
```

To solve this problem using Gurobi in Python, we will use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="red_bean_bags")
x2 = m.addVar(vtype=GRB.INTEGER, name="blue_bean_bags")

# Set the objective function
m.setObjective(5*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 >= 3, "at_least_3_red")
m.addConstr(x2 >= 2, "at_least_2_blue")
m.addConstr(x1 <= 8, "at_most_8_red")
m.addConstr(x2 <= 8, "at_most_8_blue")
m.addConstr(x1 + x2 == 12, "total_bean_bags")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Red bean bags: {x1.x}")
    print(f"Blue bean bags: {x2.x}")
    print(f"Total points: {5*x1.x + 8*x2.x}")
else:
    print("No optimal solution found")
```