## Problem Description and Formulation

The problem is an optimization problem that involves maximizing an objective function subject to several constraints. The objective function to be maximized is:

\[ 9 \times \text{orange trees} + 8 \times \text{basil plants} + 3 \times \text{apple trees} \]

The constraints are:

1. **Water Need Constraints:**
   - Orange trees need 7 inches of water per week each.
   - Basil plants need 17 inches of water per week each.
   - Apple trees need 12 inches of water per week each.
   - The total water need must be at least 38 inches per week.
   - The maximum water available for orange and apple trees is 162 inches per week.
   - The total water need of orange and basil plants must be maximum 78 inches per week.
   - The maximum water available for basil and apple trees is 131 inches per week.
   - The total water need of all three must be no more than 219 inches per week.

2. **Beauty Rating Constraints:**
   - The beauty rating of orange trees is 7 each.
   - The beauty rating of basil plants is 16 each.
   - The beauty rating of apple trees is 13 each.
   - The total combined beauty rating from orange and basil plants should be at maximum 218.
   - The total combined beauty rating from basil and apple trees must be 205 at a maximum.
   - The total combined beauty rating from all three should be equal to or less than 205.

3. **Integer Constraints:**
   - An integer number of orange trees must be used.
   - You must use an integer amount of basil plants.
   - You are limited to an integer amount of apple trees.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define the variables
    orange_trees = model.addVar(lb=0, ub=None, vtype=gurobi.GRB.INTEGER, name="orange_trees")
    basil_plants = model.addVar(lb=0, ub=None, vtype=gurobi.GRB.INTEGER, name="basil_plants")
    apple_trees = model.addVar(lb=0, ub=None, vtype=gurobi.GRB.INTEGER, name="apple_trees")

    # Objective function
    model.setObjective(9 * orange_trees + 8 * basil_plants + 3 * apple_trees, gurobi.GRB.MAXIMIZE)

    # Water need constraints
    model.addConstr(7 * orange_trees + 17 * basil_plants + 12 * apple_trees >= 38, name="water_need_min")
    model.addConstr(7 * orange_trees + 12 * apple_trees <= 162, name="water_orange_apple_max")
    model.addConstr(7 * orange_trees + 17 * basil_plants <= 78, name="water_orange_basil_max")
    model.addConstr(17 * basil_plants + 12 * apple_trees <= 131, name="water_basil_apple_max")
    model.addConstr(7 * orange_trees + 17 * basil_plants + 12 * apple_trees <= 219, name="water_total_max")

    # Beauty rating constraints
    model.addConstr(7 * orange_trees + 16 * basil_plants <= 218, name="beauty_orange_basil_max")
    model.addConstr(16 * basil_plants + 13 * apple_trees <= 205, name="beauty_basil_apple_max")
    model.addConstr(7 * orange_trees + 16 * basil_plants + 13 * apple_trees <= 205, name="beauty_total_max")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal Solution:")
        print(f"Orange Trees: {orange_trees.varValue}")
        print(f"Basil Plants: {basil_plants.varValue}")
        print(f"Apple Trees: {apple_trees.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```