## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'strips of bacon' and 'green beans'. Let's denote 'strips of bacon' as $x_1$ and 'green beans' as $x_2$. The objective function to minimize is $7x_1^2 + 8x_1x_2 + 6x_2^2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $1.27x_1$ (grams of fiber from strips of bacon)
- $1.62x_1$ (milligrams of iron from strips of bacon)
- $11.41x_1$ (milligrams of calcium from strips of bacon)
- $7.15x_2$ (grams of fiber from green beans)
- $10.55x_2$ (milligrams of iron from green beans)
- $6.62x_2$ (milligrams of calcium from green beans)
- $1.27x_1^2 + 7.15x_2^2 \geq 62$ (at least 62 grams of fiber from $x_1^2$ and $x_2^2$)
- $1.27x_1 + 7.15x_2 \geq 62$ (at least 62 grams of fiber from $x_1$ and $x_2$)
- $1.62^2x_1^2 + 10.55^2x_2^2 \geq 24$ (at least 24 milligrams of iron from $x_1^2$ and $x_2^2$)
- $1.62x_1 + 10.55x_2 \geq 24$ (at least 24 milligrams of iron from $x_1$ and $x_2$)
- $11.41^2x_1^2 + 6.62^2x_2^2 \geq 28$ (at least 28 milligrams of calcium from $x_1^2$ and $x_2^2$)
- $11.41x_1 + 6.62x_2 \geq 28$ (at least 28 milligrams of calcium from $x_1$ and $x_2$)
- $4x_1 - 3x_2 \geq 0$
- $1.27x_1 + 7.15x_2 \leq 157$ (at most 157 grams of fiber)
- $1.62x_1 + 10.55x_2 \leq 122$ (at most 122 milligrams of iron)
- $11.41^2x_1^2 + 6.62^2x_2^2 \leq 146$ (at most 146 milligrams of calcium squared)

## 3: Correct and simplify constraints for accurate representation
Correcting and simplifying the constraints for accurate representation:
- The actual constraints from the problem statement regarding upper bounds are:
  - $r0: 1.27x_1 + 7.15x_2 \leq 157$
  - $r1: 1.62x_1 + 10.55x_2 \leq 122$
  - $r2: 11.41x_1 + 6.62x_2 \leq 146$ (not squared in the original problem)

## 4: Symbolic representation
The symbolic representation is:
```json
{
  'sym_variables': [('x1', 'strips of bacon'), ('x2', 'green beans')],
  'objective_function': '7*x1^2 + 8*x1*x2 + 6*x2^2',
  'constraints': [
    '1.27*x1^2 + 7.15*x2^2 >= 62',
    '1.27*x1 + 7.15*x2 >= 62',
    '1.62^2*x1^2 + 10.55^2*x2^2 >= 24',
    '1.62*x1 + 10.55*x2 >= 24',
    '11.41^2*x1^2 + 6.62^2*x2^2 >= 28',
    '11.41*x1 + 6.62*x2 >= 28',
    '4*x1 - 3*x2 >= 0',
    '1.27*x1 + 7.15*x2 <= 157',
    '1.62*x1 + 10.55*x2 <= 122',
    '11.41*x1 + 6.62*x2 <= 146'
  ]
}
```

## 5: Gurobi Code
Now, let's implement this in Gurobi:
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(name="strips_of_bacon", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="green_beans", lb=0, ub=gurobi.GRB.INFINITY, integrality=gurobi.GRB.INTEGER)
    
    # Objective function
    model.setObjective(7*x1**2 + 8*x1*x2 + 6*x2**2, gurobi.GRB.MINIMIZE)
    
    # Constraints
    model.addConstr(1.27*x1**2 + 7.15*x2**2 >= 62)
    model.addConstr(1.27*x1 + 7.15*x2 >= 62)
    model.addConstr((1.62*x1)**2 + (10.55*x2)**2 >= 24)
    model.addConstr(1.62*x1 + 10.55*x2 >= 24)
    model.addConstr((11.41*x1)**2 + (6.62*x2)**2 >= 28)
    model.addConstr(11.41*x1 + 6.62*x2 >= 28)
    model.addConstr(4*x1 - 3*x2 >= 0)
    model.addConstr(1.27*x1 + 7.15*x2 <= 157)
    model.addConstr(1.62*x1 + 10.55*x2 <= 122)
    model.addConstr(11.41*x1 + 6.62*x2 <= 146)
    
    # Optimize
    model.optimize()
    
    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Strips of bacon: ", x1.varValue)
        print("Green beans: ", x2.varValue)
    else:
        print("No solution found")

optimize_problem()
```