## Symbolic Representation

The problem involves maximizing profit from packaging fish meat and shrimp meat under certain machine availability constraints. Let's denote:

- $x_1$ as the number of packages of fish meat
- $x_2$ as the number of packages of shrimp meat

The profit from a package of fish meat is $7, and from a package of shrimp meat is $3. Therefore, the objective function to maximize profit is:

\[ \text{Maximize:} \quad 7x_1 + 3x_2 \]

Each package of fish meat requires 3 minutes in the weight checking machine and 15 minutes in the packaging inspection machine. Each package of shrimp meat requires 1.5 minutes in the weight checking machine and 7 minutes in the packaging inspection machine. Given that each machine is available for at most 1200 minutes a week, the constraints are:

\[ 3x_1 + 1.5x_2 \leq 1200 \]
\[ 15x_1 + 7x_2 \leq 1200 \]

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

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'fish meat packages'), ('x2', 'shrimp meat packages')],
    'objective_function': '7*x1 + 3*x2',
    'constraints': [
        '3*x1 + 1.5*x2 <= 1200',
        '15*x1 + 7*x2 <= 1200',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

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

# Objective function: Maximize 7*x1 + 3*x2
model.setObjective(7*x1 + 3*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(3*x1 + 1.5*x2 <= 1200, name="weight_checking_constraint")
model.addConstr(15*x1 + 7*x2 <= 1200, name="packaging_inspection_constraint")

# Solve the model
model.optimize()

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