To solve this optimization problem, we first need to translate the natural language description into a symbolic representation. Let's define our variables as follows:

- $x_1$ represents the number of reams of lined paper.
- $x_2$ represents the number of reams of graph paper.

The objective function aims to maximize profit. Given that there is a profit of $11 per ream of lined paper and $13 per ream of graph paper, our objective function can be written as:

\[ \text{Maximize} \quad 11x_1 + 13x_2 \]

Now, let's consider the constraints. Each machine (cutting and line-printing) has a limited availability of 3500 minutes per week.

- The cutting machine constraint: A ream of lined paper requires 2 minutes on the cutting machine, and a ream of graph paper also requires 2 minutes. Thus, the total time used by the cutting machine is $2x_1 + 2x_2$, which must be less than or equal to 3500 minutes.
  
- The line-printing machine constraint: A ream of lined paper requires 6 minutes on the line-printing machine, and a ream of graph paper requires 10 minutes. Thus, the total time used by the line-printing machine is $6x_1 + 10x_2$, which must also be less than or equal to 3500 minutes.

Additionally, we have non-negativity constraints since the number of reams cannot be negative:

\[ x_1 \geq 0, \quad x_2 \geq 0 \]

Thus, our symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of reams of lined paper'), ('x2', 'number of 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']
}
```

Here is the Gurobi code in Python to solve this linear programming problem:
```python
from gurobipy import *

# Create a new model
m = Model("Paper_Company_Optimization")

# Define variables
x1 = m.addVar(lb=0, name="lined_paper")
x2 = m.addVar(lb=0, name="graph_paper")

# Set the objective function
m.setObjective(11*x1 + 13*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 + 2*x2 <= 3500, "cutting_machine")
m.addConstr(6*x1 + 10*x2 <= 3500, "line_printing_machine")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of reams of lined paper: {x1.x}")
    print(f"Number of reams of graph paper: {x2.x}")
    print(f"Maximum profit: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```