To solve this problem, we first need to define the symbolic representation of the variables and the optimization problem.

Let's denote:
- $x_1$ as the amount of Seasoning A (in kg) that the chef should buy.
- $x_2$ as the amount of Seasoning B (in kg) that the chef should buy.

The objective function is to minimize the total cost, which can be represented algebraically as:
\[ 1.5x_1 + 3x_2 \]

The constraints based on the problem description are:
1. The new mixture must contain a minimum of 5 units of pepper.
   Given that Seasoning A contains 2 units of pepper per kg and Seasoning B contains 1 unit of pepper per kg, we have:
   \[ 2x_1 + x_2 \geq 5 \]
2. The new mixture must contain a minimum of 6 units of salt.
   Given that Seasoning A contains 1 unit of salt per kg and Seasoning B contains 4 units of salt per kg, we have:
   \[ x_1 + 4x_2 \geq 6 \]
3. The amount of each seasoning bought cannot be negative (non-negativity constraint):
   \[ x_1 \geq 0 \]
   \[ x_2 \geq 0 \]

Thus, the symbolic representation of the problem in JSON format is:
```json
{
  'sym_variables': [('x1', 'Seasoning A'), ('x2', 'Seasoning B')],
  'objective_function': '1.5*x1 + 3*x2',
  'constraints': ['2*x1 + x2 >= 5', 'x1 + 4*x2 >= 6', 'x1 >= 0', 'x2 >= 0']
}
```

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

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

# Add variables
x1 = m.addVar(name="Seasoning_A", vtype=GRB.CONTINUOUS, lb=0)
x2 = m.addVar(name="Seasoning_B", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function
m.setObjective(1.5*x1 + 3*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x1 + x2 >= 5, name="pepper_constraint")
m.addConstr(x1 + 4*x2 >= 6, name="salt_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Seasoning A: {x1.x} kg")
    print(f"Seasoning B: {x2.x} kg")
    print(f"Total cost: ${1.5*x1.x + 3*x2.x:.2f}")
else:
    print("No optimal solution found.")
```