## Problem Description and Formulation

The problem is a linear programming optimization problem. The goal is to maximize profit by determining the optimal number of acres to allocate to growing lavender and tulips, given certain constraints.

### Decision Variables

- \(L\): The number of acres allocated to lavender.
- \(T\): The number of acres allocated to tulips.

### Objective Function

The objective is to maximize profit. Given that the profit per acre of lavender is $250 and the profit per acre of tulips is $200, the objective function can be formulated as:

\[ \text{Maximize:} \quad 250L + 200T \]

### Constraints

1. **Total Acres Constraint**: The gardener has 50 acres available.
\[ L + T \leq 50 \]

2. **Minimum Lavender Constraint**: The gardener must grow at least 5 acres of lavender.
\[ L \geq 5 \]

3. **Minimum Tulips Constraint**: The gardener must grow at least 8 acres of tulips.
\[ T \geq 8 \]

4. **Lavender vs. Tulips Constraint**: The gardener can grow at most twice the amount of lavender as tulips.
\[ L \leq 2T \]

## Gurobi Code

```python
import gurobipy as gp

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

# Define the decision variables
L = model.addVar(lb=5, name="Lavender_Acres")  # At least 5 acres of lavender
T = model.addVar(lb=8, name="Tulips_Acres")    # At least 8 acres of tulips

# Objective function: Maximize profit
model.setObjective(250*L + 200*T, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(L + T <= 50, name="Total_Acres")  # Total acres constraint
model.addConstr(L <= 2*T, name="Lavender_vs_Tulips")  # Lavender vs. tulips constraint

# Solve the model
model.solve()

# Output the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal Solution:")
    print(f"Lavender Acres: {L.varValue}")
    print(f"Tulips Acres: {T.varValue}")
    print(f"Max Profit: ${250*L.varValue + 200*T.varValue}")
else:
    print("No optimal solution found.")
```