## Problem Description and Symbolic Representation

First, let's convert the natural language description into a symbolic representation.

### Variables:
- $x_1$ = Number of dresses
- $x_2$ = Number of suits

### Objective Function:
The objective is to maximize profit. Given that the profit per dress is $500 and the profit per suit is $800, the objective function can be represented as:
\[ \text{Maximize:} \quad 500x_1 + 800x_2 \]

### Constraints:
1. Sewing machine hours: $2x_1 + x_2 \leq 30$
2. Embroidery machine hours: $4x_1 + x_2 \leq 50$
3. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'dresses'), ('x2', 'suits')],
    'objective_function': '500*x1 + 800*x2',
    'constraints': [
        '2*x1 + x2 <= 30',
        '4*x1 + x2 <= 50',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_production_problem():
    # Create a new model
    model = gp.Model("production_problem")

    # Define variables
    x1 = model.addVar(name="dresses", lb=0, vtype=gp.GRB.CONTINUOUS)
    x2 = model.addVar(name="suits", lb=0, vtype=gp.GRB.CONTINUOUS)

    # Objective function: Maximize profit
    model.setObjective(500*x1 + 800*x2, gp.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2*x1 + x2 <= 30, name="sewing_machine_hours")
    model.addConstr(4*x1 + x2 <= 50, name="embroidery_machine_hours")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal production: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Max Profit: ${model.objVal:.2f}")
    else:
        print("The model is infeasible.")

solve_production_problem()
```