## Problem Description and Formulation

The flower grower has 120 acres of land to plant tulips and orchids. The goal is to maximize profit given the costs and profits per acre for each type of flower, along with a budget constraint of $1200 for seeds.

### Variables
- Let \(T\) be the number of acres planted with tulips.
- Let \(O\) be the number of acres planted with orchids.

### Objective Function
The profit per acre of tulips is $75, and for orchids, it is $105. The objective is to maximize the total profit \(P\):
\[ P = 75T + 105O \]

### Constraints
1. **Land Constraint**: The grower has 120 acres of land.
\[ T + O \leq 120 \]
2. **Budget Constraint**: The seed for tulips costs $15 per acre, and for orchids, it costs $40 per acre. The total budget is $1200.
\[ 15T + 40O \leq 1200 \]
3. **Non-Negativity Constraints**: The acres planted cannot be negative.
\[ T \geq 0, O \geq 0 \]

## Gurobi Code

To solve this linear programming problem using Gurobi in Python, we will use the Gurobi Python interface. First, ensure you have Gurobi installed and a valid license.

```python
import gurobi

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

    # Define variables
    T = model.addVar(lb=0, name="Tulips")
    O = model.addVar(lb=0, name="Orchids")

    # Objective function: Maximize profit
    model.setObjective(75 * T + 105 * O, gurobi.GRB.MAXIMIZE)

    # Land constraint
    model.addConstr(T + O <= 120, name="Land_Constraint")

    # Budget constraint
    model.addConstr(15 * T + 40 * O <= 1200, name="Budget_Constraint")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal acres of Tulips: {T.varValue}")
        print(f"Optimal acres of Orchids: {O.varValue}")
        print(f"Max Profit: ${model.objVal}")
    else:
        print("The problem is infeasible")

solve_flower_planting_problem()
```

This code defines the problem using Gurobi's Python API, sets up the objective function and constraints, and then solves the optimization problem. The solution provides the optimal number of acres for tulips and orchids to maximize profit within the given constraints.