To tackle this problem, we first need to understand and translate the given natural language description into a symbolic representation of an optimization problem. This involves defining variables, an objective function, and constraints.

### Symbolic Representation

Let's denote:
- $x_1$ as 'hours worked by Bobby',
- $x_2$ as 'hours worked by Bill'.

The objective function to maximize is: $8x_1 + 5x_2$

Given the constraints:
1. Work quality rating for Bobby: $7x_1$
2. Organization score for Bobby: $21x_1$
3. Work quality rating for Bill: $27x_2$
4. Organization score for Bill: $26x_2$
5. Combined work quality rating $\geq 49$: $7x_1 + 27x_2 \geq 49$
6. Combined organization score $\geq 50$: $21x_1 + 26x_2 \geq 50$
7. Constraint on hours worked: $-4x_1 + 3x_2 \geq 0$
8. Maximum combined work quality rating $\leq 93$: $7x_1 + 27x_2 \leq 93$
9. Maximum combined organization score $\leq 115$: $21x_1 + 26x_2 \leq 115$

Since the problem specifies that $x_1$ can be non-integer but $x_2$ must be integer, we have:
- $x_1 \in \mathbb{R}$ (real numbers)
- $x_2 \in \mathbb{Z}$ (integers)

### Symbolic Representation in JSON Format

```json
{
  'sym_variables': [('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Bill')],
  'objective_function': '8*x1 + 5*x2',
  'constraints': [
    '7*x1 + 27*x2 >= 49',
    '21*x1 + 26*x2 >= 50',
    '-4*x1 + 3*x2 >= 0',
    '7*x1 + 27*x2 <= 93',
    '21*x1 + 26*x2 <= 115'
  ]
}
```

### Gurobi Code

To solve this optimization problem using Gurobi, we need to define the model, variables, objective function, and constraints accordingly. Here's how you can do it in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Work Hours Optimization")

# Define variables
x1 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="hours_worked_by_Bobby")
x2 = m.addVar(lb=0, ub=GRB.INFINITY, vtype=GRB.INTEGER, name="hours_worked_by_Bill")

# Define the objective function
m.setObjective(8*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(7*x1 + 27*x2 >= 49, "work_quality_rating")
m.addConstr(21*x1 + 26*x2 >= 50, "organization_score_min")
m.addConstr(-4*x1 + 3*x2 >= 0, "hours_worked_constraint")
m.addConstr(7*x1 + 27*x2 <= 93, "work_quality_rating_max")
m.addConstr(21*x1 + 26*x2 <= 115, "organization_score_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Bobby: {x1.x}")
    print(f"Hours worked by Bill: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```