## Step 1: Define the symbolic representation of the variables
The variables are 'bean stalks', 'orange trees', 'pansies', 'apple trees', which can be represented symbolically as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7.64x_1 + 4.45x_2 + 6.11x_3 + 7.77x_4$.

## Step 3: Define the resilience index for each variable
The resilience indices are given as:
- $x_1$ (bean stalks): 14.59
- $x_2$ (orange trees): 19.86
- $x_3$ (pansies): 17.7
- $x_4$ (apple trees): 8.06

## 4: Convert the constraints into a symbolic representation
The constraints are:
1. $14.59x_1 + 17.7x_3 \geq 21$
2. $14.59x_1 + 8.06x_4 \geq 51$
3. $14.59x_1 + 19.86x_2 \geq 43$
4. $19.86x_2 + 8.06x_4 \geq 49$
5. $14.59x_1 + 19.86x_2 + 17.7x_3 \geq 50$
6. $19.86x_2 + 17.7x_3 + 8.06x_4 \geq 50$
7. $14.59x_1 + 19.86x_2 + 17.7x_3 \geq 25$
8. $19.86x_2 + 17.7x_3 + 8.06x_4 \geq 25$
9. $14.59x_1 + 19.86x_2 + 17.7x_3 + 8.06x_4 \geq 25$
10. $-3x_1 + x_3 \geq 0$
11. $-7x_2 + 2x_3 \geq 0$
12. $x_1, x_2, x_3, x_4$ are integers.

## 5: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'bean stalks'), ('x2', 'orange trees'), ('x3', 'pansies'), ('x4', 'apple trees')],
'objective_function': '7.64*x1 + 4.45*x2 + 6.11*x3 + 7.77*x4',
'constraints': [
    '14.59*x1 + 17.7*x3 >= 21',
    '14.59*x1 + 8.06*x4 >= 51',
    '14.59*x1 + 19.86*x2 >= 43',
    '19.86*x2 + 8.06*x4 >= 49',
    '14.59*x1 + 19.86*x2 + 17.7*x3 >= 50',
    '19.86*x2 + 17.7*x3 + 8.06*x4 >= 50',
    '14.59*x1 + 19.86*x2 + 17.7*x3 >= 25',
    '19.86*x2 + 17.7*x3 + 8.06*x4 >= 25',
    '14.59*x1 + 19.86*x2 + 17.7*x3 + 8.06*x4 >= 25',
    '-3*x1 + x3 >= 0',
    '-7*x2 + 2*x3 >= 0'
]
}
```

## 6: Implement the problem in Gurobi
```python
import gurobi

# Define the model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name='bean_stalks', vtype=gurobi.GRB.INTEGER)
x2 = model.addVar(name='orange_trees', vtype=gurobi.GRB.INTEGER)
x3 = model.addVar(name='pansies', vtype=gurobi.GRB.INTEGER)
x4 = model.addVar(name='apple_trees', vtype=gurobi.GRB.INTEGER)

# Define the objective function
model.setObjective(7.64*x1 + 4.45*x2 + 6.11*x3 + 7.77*x4, gurobi.GRB.MINIMIZE)

# Define the constraints
model.addConstr(14.59*x1 + 17.7*x3 >= 21)
model.addConstr(14.59*x1 + 8.06*x4 >= 51)
model.addConstr(14.59*x1 + 19.86*x2 >= 43)
model.addConstr(19.86*x2 + 8.06*x4 >= 49)
model.addConstr(14.59*x1 + 19.86*x2 + 17.7*x3 >= 50)
model.addConstr(19.86*x2 + 17.7*x3 + 8.06*x4 >= 50)
model.addConstr(14.59*x1 + 19.86*x2 + 17.7*x3 >= 25)
model.addConstr(19.86*x2 + 17.7*x3 + 8.06*x4 >= 25)
model.addConstr(14.59*x1 + 19.86*x2 + 17.7*x3 + 8.06*x4 >= 25)
model.addConstr(-3*x1 + x3 >= 0)
model.addConstr(-7*x2 + 2*x3 >= 0)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objval)
    print('bean stalks: ', x1.varValue)
    print('orange trees: ', x2.varValue)
    print('pansies: ', x3.varValue)
    print('apple trees: ', x4.varValue)
else:
    print('The model is infeasible')
```