## Problem Description and Symbolic Representation

The problem involves a company that produces regular desks and standing desks. The goal is to maximize profit given the constraints on wood and packaging time.

### Symbolic Variables:
- $x_1$ : regular desks
- $x_2$ : standing desks

### Objective Function:
The profit per regular desk is $200, and the profit per standing desk is $300. Therefore, the objective function to maximize profit is:
\[ \text{Maximize:} \quad 200x_1 + 300x_2 \]

### Constraints:
1. Wood constraint: Regular desks require 20 units of wood, and standing desks require 15 units of wood. The company has 4000 units of wood available.
\[ 20x_1 + 15x_2 \leq 4000 \]

2. Packaging time constraint: Regular desks take 10 minutes to package, and standing desks take 20 minutes to package. The company has 1500 minutes of packaging time available.
\[ 10x_1 + 20x_2 \leq 1500 \]

3. Non-negativity constraints:
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'regular desks'), ('x2', 'standing desks')],
    'objective_function': '200*x1 + 300*x2',
    'constraints': [
        '20*x1 + 15*x2 <= 4000',
        '10*x1 + 20*x2 <= 1500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

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

    # Objective function: Maximize profit
    model.setObjective(200 * x1 + 300 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(20 * x1 + 15 * x2 <= 4000, name="wood_constraint")
    model.addConstr(10 * x1 + 20 * x2 <= 1500, name="packaging_time_constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found")

solve_desk_production_problem()
```