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

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $7.28x_1^2 + 3.0x_1x_2 + 3.69x_2^2 + 8.12x_1 + 8.29x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $3.15x_1 = 3.15$ (Mary's organization score is 3.15, but this seems to be a fixed value, not a constraint in the traditional sense. It implies $x_1$ has a fixed value, but we'll consider it as $3.15 - 3.15x_1 = 0$ for consistency)
- $2.73x_1 = 2.73$ (Mary's paperwork competence rating is 2.73, similarly, $2.73 - 2.73x_1 = 0$)
- $3.19x_2 = 3.19$ (Jean's organization score is 3.19, $3.19 - 3.19x_2 = 0$)
- $1.4x_2 = 1.4$ (Jean's paperwork competence rating is 1.4, $1.4 - 1.4x_2 = 0$)
- $3.15x_1 + 3.19x_2 \geq 5$ (total combined organization score)
- $2.73x_1 + 1.4x_2 \geq 18$ (total combined paperwork competence rating)
- $-x_1 + 7x_2 \geq 0$
- $3.15x_1 + 3.19x_2 \leq 21$ (total combined organization score)
- $2.73x_1 + 1.4x_2 \leq 36$ (total combined paperwork competence rating)

However, given that $x_1$ and $x_2$ seem to have fixed values based on the initial conditions, let's reassess:
- The actual constraints from the problem statement that involve $x_1$ and $x_2$ directly as variables are:
  - $3.15x_1 = 3.15$
  - $2.73x_1 = 2.73$
  - $3.19x_2 = 3.19$
  - $1.4x_2 = 1.4$

These imply $x_1 = 1$ and $x_2 = 1$ directly.

## 4: Realization of direct assignment
Given $x_1 = 1$ and $x_2 = 1$:
- The organization score constraint becomes $3.15*1 + 3.19*1 = 6.34 \geq 5$ (satisfied)
- The paperwork competence rating constraint becomes $2.73*1 + 1.4*1 = 4.13 \geq 18$ (not satisfied)

## 5: Conclusion on feasibility
Since $2.73*1 + 1.4*1 = 4.13$ is less than 18, the problem as stated with the given "fixed" values for $x_1$ and $x_2$ is infeasible.

## 6: Symbolic Representation
Given the misunderstanding in steps, let's correct and simplify:
- $\text{sym_variables}: [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Jean')]$
- $\text{objective_function}: 7.28x1^2 + 3.0x1x2 + 3.69x2^2 + 8.12x1 + 8.29x2$
- $\text{constraints}: [3.15x1 - 3.15 = 0, 2.73x1 - 2.73 = 0, 3.19x2 - 3.19 = 0, 1.4x2 - 1.4 = 0, 3.15x1 + 3.19x2 >= 5, 2.73x1 + 1.4x2 >= 18, -x1 + 7x2 >= 0, 3.15x1 + 3.19x2 <= 21, 2.73x1 + 1.4x2 <= 36]$

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

def optimization_problem():
    model = gurobi.Model()
    
    # Variables
    x1 = model.addVar(name="hours_worked_by_Mary", vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="hours_worked_by_Jean", vtype=gurobi.GRB.CONTINUOUS)
    
    # Objective function
    model.setObjective(7.28*x1**2 + 3.0*x1*x2 + 3.69*x2**2 + 8.12*x1 + 8.29*x2, gurobi.GRB.MAXIMIZE)
    
    # Constraints
    model.addConstr(3.15*x1 == 3.15, name="Mary_organization_score")
    model.addConstr(2.73*x1 == 2.73, name="Mary_paperwork_competence_rating")
    model.addConstr(3.19*x2 == 3.19, name="Jean_organization_score")
    model.addConstr(1.4*x2 == 1.4, name="Jean_paperwork_competence_rating")
    model.addConstr(3.15*x1 + 3.19*x2 >= 5, name="total_organization_score_min")
    model.addConstr(2.73*x1 + 1.4*x2 >= 18, name="total_paperwork_competence_rating_min")
    model.addConstr(-x1 + 7*x2 >= 0, name="hours_worked_constraint")
    model.addConstr(3.15*x1 + 3.19*x2 <= 21, name="total_organization_score_max")
    model.addConstr(2.73*x1 + 1.4*x2 <= 36, name="total_paperwork_competence_rating_max")
    
    # Solve the model
    model.optimize()
    
    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Mary: ", x1.varValue)
        print("Hours worked by Jean: ", x2.varValue)
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible")
    else:
        print("The model has a non-optimal status")

optimization_problem()
```

The final answer is: 
```json
{
    'sym_variables': [('x1', 'hours worked by Mary'), ('x2', 'hours worked by Jean')],
    'objective_function': '7.28*x1^2 + 3.0*x1*x2 + 3.69*x2^2 + 8.12*x1 + 8.29*x2',
    'constraints': [
        '3.15*x1 - 3.15 = 0', 
        '2.73*x1 - 2.73 = 0', 
        '3.19*x2 - 3.19 = 0', 
        '1.4*x2 - 1.4 = 0', 
        '3.15*x1 + 3.19*x2 >= 5', 
        '2.73*x1 + 1.4*x2 >= 18', 
        '-x1 + 7*x2 >= 0', 
        '3.15*x1 + 3.19*x2 <= 21', 
        '2.73*x1 + 1.4*x2 <= 36'
    ]
}
```