## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and their corresponding natural language objects:
- $x_0$ represents 'kiwis'
- $x_1$ represents 'eggs'
- $x_2$ represents 'cherry pies'

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $3 \cdot x_0 \cdot x_1 + 2 \cdot x_0 + 4 \cdot x_1$.

## 3: List the constraints in symbolic notation
The constraints given are:
- $11x_0 + 6x_1 \leq 172$
- $11x_0 + 3x_2 \leq 141$
- $11x_0 + 6x_1 + 3x_2 \leq 141$
- $5x_1 + 7x_2 \leq 82$
- $x_0^2 + x_1^2 \leq 83$
- $x_0 + x_1 + x_2 \leq 83$
- $x_0^2 + x_1^2 \leq 84$
- $x_0^2 + x_1^2 + x_2^2 \leq 175$
- $4x_0 + 9x_1 + 3x_2 \leq 175$
- $x_0, x_1, x_2$ are non-negative and can be non-integer.

## 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'kiwis'), ('x1', 'eggs'), ('x2', 'cherry pies')],
    'objective_function': '3 * x0 * x1 + 2 * x0 + 4 * x1',
    'constraints': [
        '11 * x0 + 6 * x1 <= 172',
        '11 * x0 + 3 * x2 <= 141',
        '11 * x0 + 6 * x1 + 3 * x2 <= 141',
        '5 * x1 + 7 * x2 <= 82',
        'x0^2 + x1^2 <= 83',
        'x0 + x1 + x2 <= 83',
        'x0^2 + x1^2 <= 84',
        'x0^2 + x1^2 + x2^2 <= 175',
        '4 * x0 + 9 * x1 + 3 * x2 <= 175'
    ]
}
```

## Step 5: Write the Gurobi code for the optimization problem
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    kiwis = model.addVar(name="kiwis", lb=0)
    eggs = model.addVar(name="eggs", lb=0)
    cherry_pies = model.addVar(name="cherry_pies", lb=0)

    # Objective function
    model.setObjective(3 * kiwis * eggs + 2 * kiwis + 4 * eggs, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(11 * kiwis + 6 * eggs <= 172)
    model.addConstr(11 * kiwis + 3 * cherry_pies <= 141)
    model.addConstr(11 * kiwis + 6 * eggs + 3 * cherry_pies <= 141)
    model.addConstr(5 * eggs + 7 * cherry_pies <= 82)
    model.addConstr(kiwis**2 + eggs**2 <= 83)
    model.addConstr(kiwis + eggs + cherry_pies <= 83)
    model.addConstr(kiwis**2 + eggs**2 <= 84)
    model.addConstr(kiwis**2 + eggs**2 + cherry_pies**2 <= 175)
    model.addConstr(4 * kiwis + 9 * eggs + 3 * cherry_pies <= 175)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Kiwis: ", kiwis.varValue)
        print("Eggs: ", eggs.varValue)
        print("Cherry Pies: ", cherry_pies.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```