## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize the points scored in an arcade shooting game by shooting deer and bears, subject to certain constraints.

### Decision Variables

Let \(D\) be the number of deer shot and \(B\) be the number of bears shot.

### Objective Function

The objective is to maximize the total points scored. Since each deer shot is 4 points and each bear shot is 10 points, the objective function can be written as:

\[ \text{Maximize:} \quad 4D + 10B \]

### Constraints

1. **Minimum Shooting Requirements:**
   - At least 5 deer must be shot: \( D \geq 5 \)
   - At least 2 bears must be shot: \( B \geq 2 \)

2. **Maximum Shooting Limits:**
   - At most 10 deer can be shot: \( D \leq 10 \)
   - At most 5 bears can be shot: \( B \leq 5 \)

3. **Total Bullets Constraint:**
   - The total number of animals shot cannot exceed 12: \( D + B \leq 12 \)

4. **Non-Negativity Constraints:**
   - \( D \geq 0 \) and \( B \geq 0 \), but these are partially covered by the minimum shooting requirements.

## Gurobi Code Formulation

Given the problem formulation, we can now translate it into Gurobi code in Python:

```python
import gurobi

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

    # Define the decision variables with their bounds
    D = model.addVar(lb=5, ub=10, name="Deer")
    B = model.addVar(lb=2, ub=5, name="Bears")

    # Objective function: Maximize 4D + 10B
    model.setObjective(4 * D + 10 * B, gurobi.GRB.MAXIMIZE)

    # Additional constraint: D + B <= 12
    model.addConstr(D + B <= 12, name="Total_Bullets")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal Solution: Deer = {D.varValue}, Bears = {B.varValue}")
        print(f"Max Points: {4 * D.varValue + 10 * B.varValue}")
    else:
        print("The model is infeasible.")

solve_arcade_shooting_game()
```

This code defines the optimization problem using Gurobi's Python interface, sets up the objective function and constraints according to the problem description, and solves the model to find the optimal shooting strategy that maximizes points.