## Step 1: Define the symbolic representation of the variables
The variables are 'planners' and 'color printers', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $7x_1 + 1x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $20x_1 + 1x_2 \geq 33$
- $7x_1 + 1x_2 \geq 56$
- $12x_1 + 19x_2 \geq 84$
- $13x_1 + 20x_2 \geq 63$
- $17x_1 + 13x_2 \geq 86$
- $-x_1 + 7x_2 \geq 0$
- $20x_1 + 1x_2 \leq 44$
- $7x_1 + 1x_2 \leq 136$
- $12x_1 + 19x_2 \leq 122$
- $13x_1 + 20x_2 \leq 100$
- $17x_1 + 13x_2 \leq 104$
- $x_1 \in \mathbb{Z}^+$, $x_2 \in \mathbb{Z}^+$

## 4: Convert the problem into Gurobi code
We will use the Gurobi Python API to model and solve this problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="planners", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="color_printers", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(7 * x1 + x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(20 * x1 + x2 >= 33, name="usefulness_rating")
m.addConstr(7 * x1 + x2 >= 56, name="dollar_cost")
m.addConstr(12 * x1 + 19 * x2 >= 84, name="employee_satisfaction_impact")
m.addConstr(13 * x1 + 20 * x2 >= 63, name="workplace_safety_impact")
m.addConstr(17 * x1 + 13 * x2 >= 86, name="weight")
m.addConstr(-x1 + 7 * x2 >= 0, name="planners_vs_color_printers")
m.addConstr(20 * x1 + x2 <= 44, name="max_usefulness_rating")
m.addConstr(7 * x1 + x2 <= 136, name="max_dollar_cost")
m.addConstr(12 * x1 + 19 * x2 <= 122, name="max_employee_satisfaction_impact")
m.addConstr(13 * x1 + 20 * x2 <= 100, name="max_workplace_safety_impact")
m.addConstr(17 * x1 + 13 * x2 <= 104, name="max_weight")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Planners: {x1.varValue}")
    print(f"Color Printers: {x2.varValue}")
    print(f"Objective Function: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Symbolic representation of the problem
The symbolic representation is as follows:
```json
{
    'sym_variables': [('x1', 'planners'), ('x2', 'color printers')],
    'objective_function': '7*x1 + x2',
    'constraints': [
        '20*x1 + x2 >= 33',
        '7*x1 + x2 >= 56',
        '12*x1 + 19*x2 >= 84',
        '13*x1 + 20*x2 >= 63',
        '17*x1 + 13*x2 >= 86',
        '-x1 + 7*x2 >= 0',
        '20*x1 + x2 <= 44',
        '7*x1 + x2 <= 136',
        '12*x1 + 19*x2 <= 122',
        '13*x1 + 20*x2 <= 100',
        '17*x1 + 13*x2 <= 104'
    ]
}
```