## Step 1: Define the symbolic representation of the variables
The variables are 'slices of pizza', 'kale salads', and 'green beans'. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $5.89x_1 + 2.73x_2 + 3.28x_3$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
1. $14.48x_1 + 11.82x_2 + 15.47x_3 \leq 137$ (total fat constraint)
2. $14.48x_1 + 11.82x_2 \geq 29$ (fat from pizza and kale salads)
3. $14.48x_1 + 11.82x_2 + 15.47x_3 \geq 29$ (fat from all three)
4. $10x_1 - 10x_3 \geq 0$ (relationship between pizza and green beans)
5. $7x_1 - 5x_2 \geq 0$ (relationship between pizza and kale salads)
6. $x_1$ is an integer (slices of pizza are whole)
7. $x_2$ is an integer (kale salads are whole)
8. $x_3$ can be fractional (green beans can be fractional)

## 4: Create the symbolic representation of the problem
```json
{
'sym_variables': [('x1', 'slices of pizza'), ('x2', 'kale salads'), ('x3', 'green beans')],
'objective_function': '5.89*x1 + 2.73*x2 + 3.28*x3',
'constraints': [
    '14.48*x1 + 11.82*x2 + 15.47*x3 <= 137',
    '14.48*x1 + 11.82*x2 >= 29',
    '14.48*x1 + 11.82*x2 + 15.47*x3 >= 29',
    '10*x1 - 10*x3 >= 0',
    '7*x1 - 5*x2 >= 0'
]
}
```

## 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name='slices_of_pizza', vtype=gurobi.GRB.INTEGER)  # slices of pizza
    x2 = model.addVar(name='kale_salads', vtype=gurobi.GRB.INTEGER)  # kale salads
    x3 = model.addVar(name='green_beans')  # green beans

    # Objective function
    model.setObjective(5.89 * x1 + 2.73 * x2 + 3.28 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(14.48 * x1 + 11.82 * x2 + 15.47 * x3 <= 137, name='total_fat')
    model.addConstr(14.48 * x1 + 11.82 * x2 >= 29, name='fat_from_pizza_and_kale')
    model.addConstr(14.48 * x1 + 11.82 * x2 + 15.47 * x3 >= 29, name='fat_from_all')
    model.addConstr(10 * x1 - 10 * x3 >= 0, name='pizza_green_beans_relationship')
    model.addConstr(7 * x1 - 5 * x2 >= 0, name='pizza_kale_relationship')

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Slices of pizza: ', x1.varValue)
        print('Kale salads: ', x2.varValue)
        print('Green beans: ', x3.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```