To solve Jake's problem, we need to convert the natural language description into a symbolic representation of the optimization problem. 

Let's define the variables:
- $x_1$ as the number of superhero figurines made
- $x_2$ as the number of cartoon figurines made

The objective function is to maximize profit, which can be represented algebraically as:
\[10x_1 + 8x_2\]

The constraints are:
- Each machine can run for at most 1000 hours. For Printer A, this translates to $5x_1 + 3x_2 \leq 1000$, and for Printer B, it's $4x_1 + 7x_2 \leq 1000$.
- Non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$, since Jake cannot make a negative number of figurines.

Thus, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'superhero figurines'), ('x2', 'cartoon figurines')],
    'objective_function': '10*x1 + 8*x2',
    'constraints': ['5*x1 + 3*x2 <= 1000', '4*x1 + 7*x2 <= 1000', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this linear programming problem, we will use the Gurobi Python library. Here is the code to find the optimal solution:
```python
from gurobipy import *

# Create a new model
m = Model("Jake's_Figurines")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="superhero_figurines", lb=0)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="cartoon_figurines", lb=0)

# Set the objective function
m.setObjective(10*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x1 + 3*x2 <= 1000, "Printer_A_Time")
m.addConstr(4*x1 + 7*x2 <= 1000, "Printer_B_Time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Superhero Figurines: {x1.x}")
    print(f"Cartoon Figurines: {x2.x}")
    print(f"Maximum Profit: {m.objVal}")
else:
    print("No optimal solution found")
```