## Step 1: Define the variables and their corresponding symbolic representation
Let's define the variables and their corresponding symbolic representation:
- $x_1$ represents 'chicken thighs'
- $x_2$ represents 'bagged salads'
- $x_3$ represents 'hamburgers'
- $x_4$ represents 'granola bars'
- $x_5$ represents 'corn cobs'

## Step 2: Formulate the objective function
The objective function to minimize is:
$8.94x_1x_2 + 3.49x_1x_4 + 6.96x_2^2 + 1.22x_2x_5 + 5.04x_3x_4 + 9.86x_3 + 1.62x_5$

## 3: Define the constraints
Constraints:
1. $5x_1 + 5x_2 + x_3 + 2x_4 + 2x_5 \leq 214$
2. $x_3^2 + x_4^2 \geq 31$
3. $5x_1 + 5x_2 \geq 24$
4. $5x_1 + 2x_4 \geq 24$
5. $5x_2 + 2x_5 \geq 23$
6. $x_3 + 2x_5 \geq 17$
7. $5x_2 + 2x_4 \geq 39$
8. $5x_1 + x_3 + 2x_5 \geq 21$
9. $x_1^2 + x_2^2 + x_5^2 \geq 21$
10. $x_3 + 2x_4 + 2x_5 \geq 21$
11. $5x_1 + x_3 + 2x_5 \geq 29$
12. $5x_1 + 5x_2 + 2x_5 \geq 29$
13. $x_3 + 2x_4 + 2x_5 \geq 29$
14. $x_1^2 + x_3^2 + x_5^2 \geq 27$
15. $5x_1 + 5x_2 + 2x_5 \geq 27$
16. $x_3^2 + x_4^2 + x_5^2 \geq 27$
17. $x_1 + x_2 + x_3 + x_4 + x_5 \geq 27$
18. $-6x_2^2 + 5x_3^2 \geq 0$
19. $-5x_3^2 + 8x_5^2 \geq 0$
20. $x_2^2 + x_3^2 \leq 204$
21. $x_3 + 2x_4 \leq 156$
22. $5x_1 + 2x_5 \leq 117$
23. $5x_2 + 2x_5 \leq 81$
24. $5x_1 + 2x_4 \leq 58$
25. $5x_1 + x_3 \leq 54$
26. $5x_1 + 5x_2 \leq 86$
27. $5x_1 + 5x_2 + 2x_5 \leq 119$
28. $x_3 + 2x_4 + 2x_5 \leq 93$
29. $x_2^2 + x_3^2 + x_5^2 \leq 103$
30. $x_1^2 + x_2^2 + x_3^2 \leq 194$

## 4: Symbolic Representation
```json
{
    'sym_variables': [
        ('x1', 'chicken thighs'), 
        ('x2', 'bagged salads'), 
        ('x3', 'hamburgers'), 
        ('x4', 'granola bars'), 
        ('x5', 'corn cobs')
    ], 
    'objective_function': '8.94*x1*x2 + 3.49*x1*x4 + 6.96*x2^2 + 1.22*x2*x5 + 5.04*x3*x4 + 9.86*x3 + 1.62*x5', 
    'constraints': [
        '5*x1 + 5*x2 + x3 + 2*x4 + 2*x5 <= 214',
        'x3^2 + x4^2 >= 31',
        '5*x1 + 5*x2 >= 24',
        '5*x1 + 2*x4 >= 24',
        '5*x2 + 2*x5 >= 23',
        'x3 + 2*x5 >= 17',
        '5*x2 + 2*x4 >= 39',
        '5*x1 + x3 + 2*x5 >= 21',
        'x1^2 + x2^2 + x5^2 >= 21',
        'x3 + 2*x4 + 2*x5 >= 21',
        '5*x1 + x3 + 2*x5 >= 29',
        '5*x1 + 5*x2 + 2*x5 >= 29',
        'x3 + 2*x4 + 2*x5 >= 29',
        'x1^2 + x3^2 + x5^2 >= 27',
        '5*x1 + 5*x2 + 2*x5 >= 27',
        'x3^2 + x4^2 + x5^2 >= 27',
        'x1 + x2 + x3 + x4 + x5 >= 27',
        '-6*x2^2 + 5*x3^2 >= 0',
        '-5*x3^2 + 8*x5^2 >= 0',
        'x2^2 + x3^2 <= 204',
        'x3 + 2*x4 <= 156',
        '5*x1 + 2*x5 <= 117',
        '5*x2 + 2*x5 <= 81',
        '5*x1 + 2*x4 <= 58',
        '5*x1 + x3 <= 54',
        '5*x1 + 5*x2 <= 86',
        '5*x1 + 5*x2 + 2*x5 <= 119',
        'x3 + 2*x4 + 2*x5 <= 93',
        'x2^2 + x3^2 + x5^2 <= 103',
        'x1^2 + x2^2 + x3^2 <= 194'
    ]
}
```

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

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

# Define the variables
x1 = m.addVar(name="chicken_thighs", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = m.addVar(name="bagged_salads", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x3 = m.addVar(name="hamburgers", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x4 = m.addVar(name="granola_bars", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x5 = m.addVar(name="corn_cobs", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Objective function
m.setObjective(8.94*x1*x2 + 3.49*x1*x4 + 6.96*x2**2 + 1.22*x2*x5 + 5.04*x3*x4 + 9.86*x3 + 1.62*x5, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(5*x1 + 5*x2 + x3 + 2*x4 + 2*x5 <= 214)
m.addConstr(x3**2 + x4**2 >= 31)
m.addConstr(5*x1 + 5*x2 >= 24)
m.addConstr(5*x1 + 2*x4 >= 24)
m.addConstr(5*x2 + 2*x5 >= 23)
m.addConstr(x3 + 2*x5 >= 17)
m.addConstr(5*x2 + 2*x4 >= 39)
m.addConstr(5*x1 + x3 + 2*x5 >= 21)
m.addConstr(x1**2 + x2**2 + x5**2 >= 21)
m.addConstr(x3 + 2*x4 + 2*x5 >= 21)
m.addConstr(5*x1 + x3 + 2*x5 >= 29)
m.addConstr(5*x1 + 5*x2 + 2*x5 >= 29)
m.addConstr(x3 + 2*x4 + 2*x5 >= 29)
m.addConstr(x1**2 + x3**2 + x5**2 >= 27)
m.addConstr(5*x1 + 5*x2 + 2*x5 >= 27)
m.addConstr(x3**2 + x4**2 + x5**2 >= 27)
m.addConstr(x1 + x2 + x3 + x4 + x5 >= 27)
m.addConstr(-6*x2**2 + 5*x3**2 >= 0)
m.addConstr(-5*x3**2 + 8*x5**2 >= 0)
m.addConstr(x2**2 + x3**2 <= 204)
m.addConstr(x3 + 2*x4 <= 156)
m.addConstr(5*x1 + 2*x5 <= 117)
m.addConstr(5*x2 + 2*x5 <= 81)
m.addConstr(5*x1 + 2*x4 <= 58)
m.addConstr(5*x1 + x3 <= 54)
m.addConstr(5*x1 + 5*x2 <= 86)
m.addConstr(5*x1 + 5*x2 + 2*x5 <= 119)
m.addConstr(x3 + 2*x4 + 2*x5 <= 93)
m.addConstr(x2**2 + x3**2 + x5**2 <= 103)
m.addConstr(x1**2 + x2**2 + x3**2 <= 194)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Chicken Thighs: ", x1.varValue)
    print("Bagged Salads: ", x2.varValue)
    print("Hamburgers: ", x3.varValue)
    print("Granola Bars: ", x4.varValue)
    print("Corn Cobs: ", x5.varValue)
else:
    print("The model is infeasible")
```