## Problem Description and Symbolic Representation

The problem involves a paper company that produces lined paper and graph paper. The production of these papers requires two machines: a cutting machine and a line-printing machine. The goal is to maximize profit given the constraints on machine availability.

### Symbolic Variables:
- $x_1$ = Number of reams of lined paper
- $x_2$ = Number of reams of graph paper

### Objective Function:
The profit per ream of lined paper is $11, and the profit per ream of graph paper is $13. Therefore, the objective function to maximize profit ($P$) is:
\[ P = 11x_1 + 13x_2 \]

### Constraints:
1. Cutting machine constraint: $2x_1 + 2x_2 \leq 3500$
2. Line-printing machine constraint: $6x_1 + 10x_2 \leq 3500$
3. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'reams of lined paper'), ('x2', 'reams of graph paper')],
    'objective_function': '11*x1 + 13*x2',
    'constraints': [
        '2*x1 + 2*x2 <= 3500',
        '6*x1 + 10*x2 <= 3500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="lined_paper", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="graph_paper", lb=0, ub=gurobi.GRB.INFINITY)

    # Objective function: Maximize profit
    model.setObjective(11*x1 + 13*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2*x1 + 2*x2 <= 3500, name="cutting_machine_constraint")
    model.addConstr(6*x1 + 10*x2 <= 3500, name="line_printing_machine_constraint")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Lined Paper: {x1.varValue}")
        print(f"Graph Paper: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("The model is infeasible or unbounded.")

solve_optimization_problem()
```