To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of chairs and shelves, formulating the objective function that represents the total profit, and listing the constraints based on the available assembly and painting time.

Let's denote:
- $x_1$ as the number of chairs
- $x_2$ as the number of shelves

The objective function, which is to maximize the total profit, can be represented as:
\[50x_1 + 55x_2\]

The constraints are based on the time available for assembly and painting:
1. Assembly time constraint: \[30x_1 + 20x_2 \leq 3000\]
2. Painting time constraint: \[50x_1 + 60x_2 \leq 4000\]

Additionally, we have non-negativity constraints since the number of chairs and shelves cannot be negative:
\[x_1 \geq 0\]
\[x_2 \geq 0\]

Now, let's represent this problem in the requested JSON format:

```json
{
    'sym_variables': [('x1', 'number of chairs'), ('x2', 'number of shelves')],
    'objective_function': '50*x1 + 55*x2',
    'constraints': ['30*x1 + 20*x2 <= 3000', '50*x1 + 60*x2 <= 4000', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="chairs")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="shelves")

# Set the objective function
m.setObjective(50*x1 + 55*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(30*x1 + 20*x2 <= 3000, "assembly_time")
m.addConstr(50*x1 + 60*x2 <= 4000, "painting_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```