## Step 1: Define the symbolic representation of the variables
The variables are: planners, staplers, color printers, headsets, cafeteria chairs.
Let's denote them as: x1, x2, x3, x4, x5 respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function is: 1.3 * planners + 8.78 * staplers + 8.21 * color printers + 4.35 * headsets + 7.78 * cafeteria chairs.
In symbolic notation, it becomes: 1.3*x1 + 8.78*x2 + 8.21*x3 + 4.35*x4 + 7.78*x5.

## Step 3: Define the constraints in symbolic notation
1. The workplace safety impact of planners is 3: 3*x1 <= 62 (but it's an equality for the impact, so just 3*x1)
2. The workplace safety impact of staplers is 6: 6*x2 
3. color printers have a workplace safety impact of 3: 3*x3
4. headsets have a workplace safety impact of 7 each: 7*x4
5. The workplace safety impact of cafeteria chairs is 3: 3*x5
6. The total combined workplace safety impact from staplers, and cafeteria chairs must be at minimum 7: 6*x2 + 3*x5 >= 7
7. The total combined workplace safety impact from color printers, and cafeteria chairs must be 4 at a minimum: 3*x3 + 3*x5 >= 4
8. The total combined workplace safety impact from planners, and staplers must be at least 8: 3*x1 + 6*x2 >= 8
9. The total combined workplace safety impact from staplers, and color printers must be equal to or greater than 10: 6*x2 + 3*x3 >= 10
10. The total combined workplace safety impact from planners, and headsets has to be 10 at a minimum: 3*x1 + 7*x4 >= 10
11. The total combined workplace safety impact from planners, and cafeteria chairs has to be 4 or more: 3*x1 + 3*x5 >= 4
12. The total combined workplace safety impact from color printers plus headsets should be greater than or equal to 4: 3*x3 + 7*x4 >= 4
13. The total combined workplace safety impact from staplers, and headsets has to be no less than 12: 6*x2 + 7*x4 >= 12
14. 2 times the number of planners, plus -6 times the number of staplers must be no less than zero: 2*x1 - 6*x2 >= 0
15. The total combined workplace safety impact from headsets and cafeteria chairs has to be 56 or less: 7*x4 + 3*x5 <= 56
16. The total combined workplace safety impact from color printers and cafeteria chairs has to be as much or less than 26: 3*x3 + 3*x5 <= 26
17. The total combined workplace safety impact from staplers, and headsets must be equal to or less than 21: 6*x2 + 7*x4 <= 21
18. The total combined workplace safety impact from planners plus color printers has to be as much or less than 13: 3*x1 + 3*x3 <= 13
19. The total combined workplace safety impact from planners plus staplers has to be 44 at maximum: 3*x1 + 6*x2 <= 44
20. The total combined workplace safety impact from planners, headsets, and cafeteria chairs must be 23 or less: 3*x1 + 7*x4 + 3*x5 <= 23
21. The total combined workplace safety impact from planners plus staplers plus color printers has to be equal to or less than 32: 3*x1 + 6*x2 + 3*x3 <= 32
22. The total combined workplace safety impact from planners, color printers and cafeteria chairs has to be 15 or less: 3*x1 + 3*x3 + 3*x5 <= 15
23. The total combined workplace safety impact from staplers, headsets and cafeteria chairs has to be 20 or less: 6*x2 + 7*x4 + 3*x5 <= 20
24. The total combined workplace safety impact from planners plus staplers plus cafeteria chairs should be 51 at maximum: 3*x1 + 6*x2 + 3*x5 <= 51
25. The total combined workplace safety impact from planners plus color printers plus headsets should be  no more than 55: 3*x1 + 3*x3 + 7*x4 <= 55
26. The total combined workplace safety impact from planners plus staplers plus headsets has to be 27 or less: 3*x1 + 6*x2 + 7*x4 <= 27
27. The total combined workplace safety impact from planners, staplers, color printers, headsets and cafeteria chairs has to be 27 at maximum: 3*x1 + 6*x2 + 3*x3 + 7*x4 + 3*x5 <= 27

## Step 4: Write down the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'planners'),
        ('x2', 'staplers'),
        ('x3', 'color printers'),
        ('x4', 'headsets'),
        ('x5', 'cafeteria chairs')
    ],
    'objective_function': '1.3*x1 + 8.78*x2 + 8.21*x3 + 4.35*x4 + 7.78*x5',
    'constraints': [
        '3*x1 <= 62',
        '6*x2 <= 62',
        '3*x3 <= 62',
        '7*x4 <= 62',
        '3*x5 <= 62',
        '6*x2 + 3*x5 >= 7',
        '3*x3 + 3*x5 >= 4',
        '3*x1 + 6*x2 >= 8',
        '6*x2 + 3*x3 >= 10',
        '3*x1 + 7*x4 >= 10',
        '3*x1 + 3*x5 >= 4',
        '3*x3 + 7*x4 >= 4',
        '6*x2 + 7*x4 >= 12',
        '2*x1 - 6*x2 >= 0',
        '7*x4 + 3*x5 <= 56',
        '3*x3 + 3*x5 <= 26',
        '6*x2 + 7*x4 <= 21',
        '3*x1 + 3*x3 <= 13',
        '3*x1 + 6*x2 <= 44',
        '3*x1 + 7*x4 + 3*x5 <= 23',
        '3*x1 + 6*x2 + 3*x3 <= 32',
        '3*x1 + 3*x3 + 3*x5 <= 15',
        '6*x2 + 7*x4 + 3*x5 <= 20',
        '3*x1 + 6*x2 + 3*x5 <= 51',
        '3*x1 + 3*x3 + 7*x4 <= 55',
        '3*x1 + 6*x2 + 7*x4 <= 27',
        '3*x1 + 6*x2 + 3*x3 + 7*x4 + 3*x5 <= 27'
    ]
}
```

## Step 5: Implement the optimization problem using Gurobi
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x1 = m.addVar(name='planners', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='staplers', vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name='color_printers', vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name='headsets', vtype=gurobi.GRB.INTEGER)
x5 = m.addVar(name='cafeteria_chairs', vtype=gurobi.GRB.INTEGER)

# Define the objective function
m.setObjective(1.3*x1 + 8.78*x2 + 8.21*x3 + 4.35*x4 + 7.78*x5, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 <= 62)
m.addConstr(6*x2 <= 62)
m.addConstr(3*x3 <= 62)
m.addConstr(7*x4 <= 62)
m.addConstr(3*x5 <= 62)
m.addConstr(6*x2 + 3*x5 >= 7)
m.addConstr(3*x3 + 3*x5 >= 4)
m.addConstr(3*x1 + 6*x2 >= 8)
m.addConstr(6*x2 + 3*x3 >= 10)
m.addConstr(3*x1 + 7*x4 >= 10)
m.addConstr(3*x1 + 3*x5 >= 4)
m.addConstr(3*x3 + 7*x4 >= 4)
m.addConstr(6*x2 + 7*x4 >= 12)
m.addConstr(2*x1 - 6*x2 >= 0)
m.addConstr(7*x4 + 3*x5 <= 56)
m.addConstr(3*x3 + 3*x5 <= 26)
m.addConstr(6*x2 + 7*x4 <= 21)
m.addConstr(3*x1 + 3*x3 <= 13)
m.addConstr(3*x1 + 6*x2 <= 44)
m.addConstr(3*x1 + 7*x4 + 3*x5 <= 23)
m.addConstr(3*x1 + 6*x2 + 3*x3 <= 32)
m.addConstr(3*x1 + 3*x3 + 3*x5 <= 15)
m.addConstr(6*x2 + 7*x4 + 3*x5 <= 20)
m.addConstr(3*x1 + 6*x2 + 3*x5 <= 51)
m.addConstr(3*x1 + 3*x3 + 7*x4 <= 55)
m.addConstr(3*x1 + 6*x2 + 7*x4 <= 27)
m.addConstr(3*x1 + 6*x2 + 3*x3 + 7*x4 + 3*x5 <= 27)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('planners: ', x1.varValue)
    print('staplers: ', x2.varValue)
    print('color_printers: ', x3.varValue)
    print('headsets: ', x4.varValue)
    print('cafeteria_chairs: ', x5.varValue)
else:
    print('No solution found')
```