## Problem Description and Formulation

The problem is a classic example of a linear programming (LP) problem. The goal is to maximize the profit of a seafood factory that packages fish meat and shrimp meat, subject to the constraints of machine availability.

Let's define the decision variables:

* $x$: number of packages of fish meat
* $y$: number of packages of shrimp meat

The objective function is to maximize the profit:

* Profit = $7x + 3y$

The constraints are:

* Weight checking machine: $3x + 1.5y \leq 1200$
* Packaging inspection machine: $15x + 7y \leq 1200$
* Non-negativity constraints: $x \geq 0, y \geq 0$

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables
    x = model.addVar(name="fish_meat", lb=0, ub=gurobi.GRB.INFINITY)
    y = model.addVar(name="shrimp_meat", lb=0, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(7 * x + 3 * y, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(3 * x + 1.5 * y <= 1200, name="weight_checking_machine")
    model.addConstr(15 * x + 7 * y <= 1200, name="packaging_inspection_machine")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Fish meat packages: {x.varValue}")
        print(f"Shrimp meat packages: {y.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_seafood_factory_problem()
```