## Step 1: Define the symbolic variables
Let's define the symbolic variables for the problem:
- $x_1$ represents the number of plates
- $x_2$ represents the number of forks

## Step 2: Translate the objective function into symbolic notation
The profit per plate is $10 and the profit per fork is $8. The objective function to maximize profit is:
\[ \text{Maximize:} \quad 10x_1 + 8x_2 \]

## 3: Translate the constraints into symbolic notation
The constraints given are:
- Each plate takes 30 minutes of woodworker time and each fork takes 20 minutes of woodworker time, with 5000 minutes available: $30x_1 + 20x_2 \leq 5000$
- The store must make at least twice the number of forks as plates: $x_2 \geq 2x_1$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 4: Express the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'plates'), ('x2', 'forks')], 
    'objective_function': '10*x1 + 8*x2', 
    'constraints': [
        '30*x1 + 20*x2 <= 5000', 
        'x2 >= 2*x1', 
        'x1 >= 0', 
        'x2 >= 0'
    ]
}
```

## 5: Implement the problem in Gurobi Python
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="plates", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="forks", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(10*x1 + 8*x2, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(30*x1 + 20*x2 <= 5000, name="woodworker_time")
    model.addConstr(x2 >= 2*x1, name="fork_to_plate_ratio")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal number of plates: {x1.varValue}")
        print(f"Optimal number of forks: {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_optimization_problem()
```