## Problem Description and Formulation

The problem is an optimization problem with the objective to minimize a linear function subject to several linear constraints. The variables are the number of sunflowers, cherry trees, and basil plants. The objective function to minimize is $1.28x_0 + 1.29x_1 + 3.61x_2$, where $x_0$, $x_1$, and $x_2$ represent the number of sunflowers, cherry trees, and basil plants, respectively.

## Constraints

The constraints given are:
- The resilience index of sunflowers is 3.98.
- The yield of sunflowers is 1.58.
- The resilience index of cherry trees is 4.75.
- The yield of cherry trees is 11.98.
- The resilience index of basil plants is 8.04.
- The yield of basil plants is 11.92.
- $3.98x_0 + 8.04x_2 \geq 23$
- $3.98x_0 + 4.75x_1 + 8.04x_2 \geq 23$
- $1.58x_0 + 11.98x_1 \geq 47$
- $11.98x_1 + 11.92x_2 \geq 56$
- $1.58x_0 + 11.98x_1 + 11.92x_2 \geq 57$
- $-5x_1 + 2x_2 \geq 0$
- $4x_0 - 3x_2 \geq 0$
- $1.58x_0 + 11.98x_1 \leq 88$
- $1.58x_0 + 11.92x_2 \leq 76$
- $x_0$ must be an integer.
- $x_1$ must be an integer.
- $x_2$ must be an integer.

However, upon closer inspection, it seems there might have been a misunderstanding in directly translating the given "resilience index" and "yield" values as constraints since they seem to be attributes of each plant type rather than constraints themselves. The actual constraints related to these attributes are the ones that involve these values in inequalities.

## Gurobi Code

```python
import gurobipy as gp

# Define the model
model = gp.Model("optimization_problem")

# Define the variables
sunflowers = model.addVar(name="sunflowers", integer=True)
cherry_trees = model.addVar(name="cherry_trees", integer=True)
basil_plants = model.addVar(name="basil_plants", integer=True)

# Objective function
model.setObjective(1.28 * sunflowers + 1.29 * cherry_trees + 3.61 * basil_plants, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(3.98 * sunflowers + 8.04 * basil_plants >= 23, name="resilience_sunflowers_basil")
model.addConstr(3.98 * sunflowers + 4.75 * cherry_trees + 8.04 * basil_plants >= 23, name="resilience_all")
model.addConstr(1.58 * sunflowers + 11.98 * cherry_trees >= 47, name="yield_sunflowers_cherry")
model.addConstr(11.98 * cherry_trees + 11.92 * basil_plants >= 56, name="yield_cherry_basil")
model.addConstr(1.58 * sunflowers + 11.98 * cherry_trees + 11.92 * basil_plants >= 57, name="yield_all")
model.addConstr(-5 * cherry_trees + 2 * basil_plants >= 0, name="cherry_basil_tradeoff")
model.addConstr(4 * sunflowers - 3 * basil_plants >= 0, name="sunflowers_basil_tradeoff")
model.addConstr(1.58 * sunflowers + 11.98 * cherry_trees <= 88, name="yield_sunflowers_cherry_limit")
model.addConstr(1.58 * sunflowers + 11.92 * basil_plants <= 76, name="yield_sunflowers_basil_limit")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Sunflowers: {sunflowers.varValue}")
    print(f"Cherry Trees: {cherry_trees.varValue}")
    print(f"Basil Plants: {basil_plants.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```