## Step 1: Define the symbolic representation of the problem
The problem involves two products: chairs and nightstands, made by two people: John and William. Let's define the symbolic variables:
- $x_1$ = number of chairs
- $x_2$ = number of nightstands

The objective is to maximize profit, with $300 profit per chair and $500 profit per nightstand. So, the objective function is: $300x_1 + 500x_2$.

## Step 2: Define the constraints based on the given information
- Each chair takes 2 hours of John's time, and each nightstand takes 5 hours of John's time. John has 30 hours available: $2x_1 + 5x_2 \leq 30$.
- Each chair takes 4 hours of William's time, and each nightstand takes 4 hours of William's time. William has 40 hours available: $4x_1 + 4x_2 \leq 40$.
- Additionally, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of chairs and nightstands cannot be negative.

## 3: Symbolic representation in JSON format
```json
{
'sym_variables': [('x1', 'chairs'), ('x2', 'nightstands')],
'objective_function': '300*x1 + 500*x2',
'constraints': [
    '2*x1 + 5*x2 <= 30',
    '4*x1 + 4*x2 <= 40',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 4: Convert the problem into Gurobi code in Python
```python
import gurobipy as gp

# Create a new model
model = gp.Model("Woodshop_Optimization")

# Define the variables
x1 = model.addVar(name="chairs", lb=0, vtype=gp.GRB.INTEGER)  # Number of chairs
x2 = model.addVar(name="nightstands", lb=0, vtype=gp.GRB.INTEGER)  # Number of nightstands

# Define the objective function
model.setObjective(300*x1 + 500*x2, gp.GRB.MAXIMIZE)

# Define the constraints
model.addConstr(2*x1 + 5*x2 <= 30, name="John's_time_constraint")
model.addConstr(4*x1 + 4*x2 <= 40, name="William's_time_constraint")

# Solve the model
model.optimize()

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