## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Peggy', 'hours worked by Bobby', and 'hours worked by John', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the given problem into a symbolic representation
The objective function to minimize is $7.79x_0^2 + 1.47x_0x_2 + 6.87x_1^2 + 8.03x_1x_2 + 4.71x_2^2 + 9.57x_0 + 3.55x_1 + 4.7x_2$.

## 3: List the constraints
1. $12x_0 \leq 295$ (Peggy's computer competence rating constraint, but it seems this is an attribute and not directly a constraint on $x_0$),
2. $9x_0 \leq 248$ (Peggy's organization score constraint),
3. $29x_1 \leq 295$ (Bobby's computer competence rating constraint),
4. $7x_1 \leq 248$ (Bobby's organization score constraint),
5. $26x_2 \leq 295$ (John's computer competence rating constraint),
6. $28x_2 \leq 248$ (John's organization score constraint),
7. $12x_0 + 29x_1 \geq 44$ (total combined computer competence rating from $x_0$ and $x_1$),
8. $12x_0 + 26x_2 \geq 72$ (total combined computer competence rating from $x_0$ and $x_2$),
9. $29x_1 + 26x_2 \geq 55$ (total combined computer competence rating from $x_1$ and $x_2$),
10. $12x_0 + 29x_1 + 26x_2 \geq 55$ (total combined computer competence rating from $x_0$, $x_1$, and $x_2$),
11. $9x_0 + 7x_1 \geq 61$ (total combined organization score from $x_0$ and $x_1$),
12. $9x_0^2 + 28x_2^2 \geq 61$ (total combined organization score from $x_0^2$ and $x_2^2$),
13. $9x_0 + 7x_1 + 28x_2 \geq 53$ (total combined organization score from $x_0$, $x_1$, and $x_2$),
14. $8x_0 - 3x_2 \geq 0$ (constraint on $x_0$ and $x_2$),
15. $12^2x_0^2 + 26^2x_2^2 \leq 129$ (total combined computer competence rating from $x_0^2$ and $x_2^2$),
16. $12^2x_0^2 + 29^2x_1^2 \leq 214$ (total combined computer competence rating from $x_0^2$ and $x_1^2$).

## 4: Correct and simplify constraints based on problem description
Upon closer inspection, constraints 1 through 6 seem to describe attributes rather than constraints. The actual constraints from the problem description should directly relate to the variables $x_0$, $x_1$, and $x_2$.

## 5: Symbolic representation
$\textbf{sym\_variables:} [('x0', 'hours worked by Peggy'), ('x1', 'hours worked by Bobby'), ('x2', 'hours worked by John')]$

$\textbf{objective\_function:} 7.79x0^2 + 1.47x0x2 + 6.87x1^2 + 8.03x1x2 + 4.71x2^2 + 9.57x0 + 3.55x1 + 4.7x2$

$\textbf{constraints:}$
- $12x_0 + 29x_1 \geq 44$
- $12x_0 + 26x_2 \geq 72$
- $29x_1 + 26x_2 \geq 55$
- $12x_0 + 29x_1 + 26x_2 \geq 55$
- $9x_0 + 7x_1 \geq 61$
- $9x_0^2 + 28x_2^2 \geq 61$
- $9x_0 + 7x_1 + 28x_2 \geq 53$
- $8x_0 - 3x_2 \geq 0$
- $144x_0^2 + 676x_2^2 \leq 129$
- $144x_0^2 + 841x_1^2 \leq 214$

## 6: Gurobi Code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Peggy
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Bobby
    x2 = model.addVar(name="x2", lb=0)  # hours worked by John

    # Objective function
    model.setObjective(7.79 * x0**2 + 1.47 * x0 * x2 + 6.87 * x1**2 + 8.03 * x1 * x2 + 4.71 * x2**2 + 9.57 * x0 + 3.55 * x1 + 4.7 * x2)

    # Constraints
    model.addConstr(12 * x0 + 29 * x1 >= 44)
    model.addConstr(12 * x0 + 26 * x2 >= 72)
    model.addConstr(29 * x1 + 26 * x2 >= 55)
    model.addConstr(12 * x0 + 29 * x1 + 26 * x2 >= 55)
    model.addConstr(9 * x0 + 7 * x1 >= 61)
    model.addConstr(9 * x0**2 + 28 * x2**2 >= 61)
    model.addConstr(9 * x0 + 7 * x1 + 28 * x2 >= 53)
    model.addConstr(8 * x0 - 3 * x2 >= 0)
    model.addConstr(144 * x0**2 + 676 * x2**2 <= 129)
    model.addConstr(144 * x0**2 + 841 * x1**2 <= 214)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Objective: ", model.objval)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
    else:
        print("The model is infeasible")

optimization_problem()
```