## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'cantaloupes' and 'potatoes', which we can represent symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $4 \cdot cantaloupes^2 + 2 \cdot cantaloupes \cdot potatoes + 9 \cdot potatoes^2 + 9 \cdot cantaloupes$. In symbolic notation, this becomes $4x_1^2 + 2x_1x_2 + 9x_2^2 + 9x_1$.

## 3: Define the constraints in symbolic notation
The constraints given are:
1. $3.42x_1 + 2.7x_2 \geq 20$ (at least 20 milligrams of calcium),
2. $3.42x_1 \geq 20$ and $2.7x_2 \geq 0$ are not explicitly stated but $3.42x_1 + 2.7x_2 \geq 20$ covers the calcium requirement,
3. $2.08x_1 + 2.45x_2 \geq 28$ (at least $28 spent),
4. $3x_1 - 10x_2 \geq 0$,
5. $3.42x_1 + 2.7x_2 \leq 60$ (no more than 60 milligrams of calcium),
6. $2.08x_1 + 2.45x_2 \leq 73$ (no more than $73 spent),
7. $x_1$ is an integer (nonfractional number of cantaloupes),
8. $x_2$ is a real number (amount of potatoes does not have to be a whole number).

## 4: Specify the symbolic variables and constraints for output
The symbolic variables are:
- $x_1$ for 'cantaloupes'
- $x_2$ for 'potatoes'

The objective function in symbolic notation is: $4x_1^2 + 2x_1x_2 + 9x_2^2 + 9x_1$.

The constraints are:
1. $3.42x_1 + 2.7x_2 \geq 20$
2. $2.08x_1 + 2.45x_2 \geq 28$
3. $3x_1 - 10x_2 \geq 0$
4. $3.42x_1 + 2.7x_2 \leq 60$
5. $2.08x_1 + 2.45x_2 \leq 73$

## 5: Create the Gurobi model and variables
We will use Gurobi to solve this optimization problem. The model will be defined with the objective function and constraints specified.

## 6: Implement the Gurobi code
```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
cantaloupes = model.addVar(name="cantaloupes", vtype=gurobi.GRB.INTEGER)
potatoes = model.addVar(name="potatoes")

# Objective function: 4*cantaloupes^2 + 2*cantaloupes*potatoes + 9*potatoes^2 + 9*cantaloupes
model.setObjective(4*cantaloupes**2 + 2*cantaloupes*potatoes + 9*potatoes**2 + 9*cantaloupes, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(3.42*cantaloupes + 2.7*potatoes >= 20, name="calcium_requirement")
model.addConstr(2.08*cantaloupes + 2.45*potatoes >= 28, name="cost_requirement")
model.addConstr(3*cantaloupes - 10*potatoes >= 0, name="cantaloupes_vs_potatoes")
model.addConstr(3.42*cantaloupes + 2.7*potatoes <= 60, name="max_calcium")
model.addConstr(2.08*cantaloupes + 2.45*potatoes <= 73, name="max_cost")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Cantaloupes: ", cantaloupes.varValue)
    print("Potatoes: ", potatoes.varValue)
else:
    print("The model is infeasible")
```

## 7: Output the symbolic representation
```json
{
    'sym_variables': [('x1', 'cantaloupes'), ('x2', 'potatoes')],
    'objective_function': '4*x1^2 + 2*x1*x2 + 9*x2^2 + 9*x1',
    'constraints': [
        '3.42*x1 + 2.7*x2 >= 20',
        '2.08*x1 + 2.45*x2 >= 28',
        '3*x1 - 10*x2 >= 0',
        '3.42*x1 + 2.7*x2 <= 60',
        '2.08*x1 + 2.45*x2 <= 73'
    ]
}
```