## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and their corresponding natural language objects:
- $x_0$ = apples
- $x_1$ = hot dogs
- $x_2$ = oranges

The objective function to minimize is $2.56x_0 + 6.29x_1 + 1.2x_2$.

## Step 2: List all constraints in symbolic notation
Constraints:
1. $18x_0 + 13x_1 + 18x_2 \geq 47$ (total protein from all but hot dogs is at least 47, corrected to reflect all sources)
2. $18x_0 + 13x_1 + 18x_2 \geq 47$ (same as 1, ensuring total protein is at least 47)
3. $24x_0 + 17x_2 \geq 46$ (tastiness from apples and oranges)
4. $10x_1 + 17x_2 \geq 77$ (tastiness from hot dogs and oranges)
5. $24x_0 + 10x_1 + 17x_2 \geq 77$ (total tastiness)
6. $-4x_1 + 2x_2 \geq 0$ (relationship between hot dogs and oranges)
7. $18x_0 + 13x_1 \leq 106$ (protein limit from apples and hot dogs)
8. $10x_1 + 17x_2 \leq 279$ (tastiness limit from hot dogs and oranges)

## 3: Correct and Refine Constraints for Accuracy
Upon review, constraints 1 and 2 are essentially the same and should reflect the minimum total protein requirement correctly. The accurate representation should consider:
- The minimum total protein: $18x_0 + 13x_1 + 18x_2 \geq 47$
- Other constraints remain as listed.

## 4: Formulate the Problem in Gurobi Code
Now, let's formulate this problem using Gurobi.

```python
import gurobi

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

# Define variables
apples = model.addVar(name="apples", vtype=gurobi.GRB.INTEGER)
hot_dogs = model.addVar(name="hot_dogs", vtype=gurobi.GRB.INTEGER)
oranges = model.addVar(name="oranges", vtype=gurobi.GRB.INTEGER)

# Objective function
model.setObjective(2.56 * apples + 6.29 * hot_dogs + 1.2 * oranges, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(18 * apples + 13 * hot_dogs + 18 * oranges >= 47)  # Total protein
model.addConstr(24 * apples + 17 * oranges >= 46)  # Tastiness from apples and oranges
model.addConstr(10 * hot_dogs + 17 * oranges >= 77)  # Tastiness from hot dogs and oranges
model.addConstr(24 * apples + 10 * hot_dogs + 17 * oranges >= 77)  # Total tastiness
model.addConstr(-4 * hot_dogs + 2 * oranges >= 0)  # Relationship between hot dogs and oranges
model.addConstr(18 * apples + 13 * hot_dogs <= 106)  # Protein limit from apples and hot dogs
model.addConstr(10 * hot_dogs + 17 * oranges <= 279)  # Tastiness limit from hot dogs and oranges

# Optimize
model.optimize()

# Print solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Apples: {apples.varValue}")
    print(f"Hot Dogs: {hot_dogs.varValue}")
    print(f"Oranges: {oranges.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Symbolic Representation
The symbolic representation of the problem is as follows:

```json
{
    'sym_variables': [('x0', 'apples'), ('x1', 'hot dogs'), ('x2', 'oranges')],
    'objective_function': '2.56*x0 + 6.29*x1 + 1.2*x2',
    'constraints': [
        '18*x0 + 13*x1 + 18*x2 >= 47',
        '24*x0 + 17*x2 >= 46',
        '10*x1 + 17*x2 >= 77',
        '24*x0 + 10*x1 + 17*x2 >= 77',
        '-4*x1 + 2*x2 >= 0',
        '18*x0 + 13*x1 <= 106',
        '10*x1 + 17*x2 <= 279'
    ]
}
```

Please note that running this requires a Gurobi environment and appropriate licensing. 

```python
import gurobi

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

# Define variables
apples = model.addVar(name="apples", vtype=gurobi.GRB.INTEGER)
hot_dogs = model.addVar(name="hot_dogs", vtype=gurobi.GRB.INTEGER)
oranges = model.addVar(name="oranges", vtype=gurobi.GRB.INTEGER)

# Objective function
model.setObjective(2.56 * apples + 6.29 * hot_dogs + 1.2 * oranges, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(18 * apples + 13 * hot_dogs + 18 * oranges >= 47)  
model.addConstr(24 * apples + 17 * oranges >= 46)  
model.addConstr(10 * hot_dogs + 17 * oranges >= 77)  
model.addConstr(24 * apples + 10 * hot_dogs + 17 * oranges >= 77)  
model.addConstr(-4 * hot_dogs + 2 * oranges >= 0)  
model.addConstr(18 * apples + 13 * hot_dogs <= 106)  
model.addConstr(10 * hot_dogs + 17 * oranges <= 279)  

# Optimize
model.optimize()

# Print solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Apples: {apples.varValue}")
    print(f"Hot Dogs: {hot_dogs.varValue}")
    print(f"Oranges: {oranges.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```