To solve this problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables as follows:

- $x_1$ represents the number of tacos sold.
- $x_2$ represents the number of burritos sold.

The objective function is to maximize profit. Given that the profit per taco is $3 and the profit per burrito is $6, the objective function can be represented algebraically as:

\[ \text{Maximize: } 3x_1 + 6x_2 \]

The constraints based on the problem description are:
1. The food truck must sell at least 50 tacos: \( x_1 \geq 50 \)
2. The food truck must sell at least 30 burritos: \( x_2 \geq 30 \)
3. The food truck can make at most 80 tacos: \( x_1 \leq 80 \)
4. The food truck can make at most 50 burritos: \( x_2 \leq 50 \)
5. The total number of items cooked cannot exceed 100: \( x_1 + x_2 \leq 100 \)

All variables are non-negative since the number of items sold cannot be negative.

Thus, the symbolic representation of the problem in JSON format is:
```json
{
    'sym_variables': [('x1', 'tacos'), ('x2', 'burritos')], 
    'objective_function': '3*x1 + 6*x2', 
    'constraints': ['x1 >= 50', 'x2 >= 30', 'x1 <= 80', 'x2 <= 50', 'x1 + x2 <= 100']
}
```

To solve this optimization problem using Gurobi in Python, we can write the following code:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=50, ub=80, vtype=GRB.INTEGER, name="tacos")
x2 = m.addVar(lb=30, ub=50, vtype=GRB.INTEGER, name="burritos")

# Set the objective function
m.setObjective(3*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, "total_items_constraint")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of tacos: {x1.x}")
    print(f"Number of burritos: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```