To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote the number of plates as \(P\) and the number of forks as \(F\). The profit per plate is $10, and the profit per fork is $8. Thus, the total profit can be represented as \(10P + 8F\).

The constraints are:
1. Time constraint: Each plate takes 30 minutes, and each fork takes 20 minutes of woodworker time. The total available time is 5000 minutes. Therefore, the time constraint can be written as \(30P + 20F \leq 5000\).
2. Forks to plates ratio: The store must make at least twice the number of forks as plates, which gives us \(F \geq 2P\).

Since we are maximizing profit and all coefficients in our objective function and constraints are positive or zero (in terms of \(P\) and \(F\)), we don't need to consider negative values for \(P\) and \(F\), implying \(P \geq 0\) and \(F \geq 0\).

Given this formulation, the optimization problem can be summarized as:
- Maximize: \(10P + 8F\)
- Subject to:
  - \(30P + 20F \leq 5000\)
  - \(F \geq 2P\)
  - \(P \geq 0\), \(F \geq 0\)

Now, we translate this problem into Gurobi code in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Wooden Plates and Forks")

# Define the decision variables
P = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Plates")
F = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="Forks")

# Set the objective function: Maximize profit
m.setObjective(10*P + 8*F, GRB.MAXIMIZE)

# Add constraints
m.addConstr(30*P + 20*F <= 5000, "Time constraint")
m.addConstr(F >= 2*P, "Forks to plates ratio")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: Plates = {P.x}, Forks = {F.x}")
    print(f"Maximum profit: ${10*P.x + 8*F.x:.2f}")
else:
    print("No optimal solution found")
```