## Symbolic Representation

The problem can be converted into a symbolic representation as follows:

Let's denote:
- $x_1$ as the number of scientific calculators produced
- $x_2$ as the number of graphing calculators produced

The objective is to maximize profit. The profit per scientific calculator is $6, and the profit per graphing calculator is $8. Therefore, the objective function can be written as:

Maximize: $6x_1 + 8x_2$

The constraints based on the available materials are:

- Silicon: $2x_1 + 4x_2 \leq 100$
- Plastic: $4x_1 + 6x_2 \leq 200$
- Silver: $x_1 + 2x_2 \leq 50$

Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of calculators produced cannot be negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'scientific calculators'), ('x2', 'graphing calculators')],
    'objective_function': '6*x1 + 8*x2',
    'constraints': [
        '2*x1 + 4*x2 <= 100',
        '4*x1 + 6*x2 <= 200',
        'x1 + 2*x2 <= 50',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="scientific_calculators", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="graphing_calculators", lb=0, vtype=gp.GRB.CONTINUOUS)

# Objective function: maximize profit
model.setObjective(6*x1 + 8*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(2*x1 + 4*x2 <= 100, name="silicon_constraint")
model.addConstr(4*x1 + 6*x2 <= 200, name="plastic_constraint")
model.addConstr(x1 + 2*x2 <= 50, name="silver_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Scientific Calculators: {x1.varValue}")
    print(f"Graphing Calculators: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("The model is infeasible or has no solution.")
```